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Unit 3 Probability & Statistics
3.1 – Introduction to Probability & Probability Trees
3.2 – Independent & Dependent Probability
3.3 – Statistical Measures of Center
3.4 – Data Representations
3.5 – Population & Samples
3.6 – Inferring, Surveying and Developing Statistical Questions
Crazy Odds
Odds of bowling a 300 game: 11,500 to 1 Odds of getting a hole in one: 5,000 to 1 Odds of being an astronaut: 13,200,000 to 1 Odds of winning an Olympic medal: 662,000 to 1 Odds of injury from fireworks: 19,556 to 1 Odds of injury from shaving: 6,585 to 1 Odds of injury from using a chain saw: 4,464 to 1 Odds of injury from mowing the lawn: 3,623 to 1 Odds of fatally slipping in bath or shower: 2,232 to 1 Odds of drowning in a bathtub: 685,000 to 1 Odds of being struck by lightning: 576,000 to 1 Odds of being killed by lightning: 2,320,000 to 1 Odds of being murdered: 18,000 to 1 Odds of being the victim of serious crime in your lifetime: 20 to 1 Odds of being born a twin in North America: 90 to 1 Odds of having your identity stolen: 200 to 1 Odds of dating a millionaire: 215 to 1 Odds of dating a supermodel: 88,000 to 1 Odds of becoming a pro athlete: 22,000 to 1 Odds of winning an Academy Award: 11,500 to 1
Odds of a meteor landing on your house: 182,138,880,000,000 to 1
3.1 NOTES Introduction to Probability & Probability Trees
Experimental probability: ____________________________________________
Theoretical probability: ______________________________________________
1 = ______________
€
12 = _______________ 0 = _________________
Ex: Ex: Ex:
How to set it up
Numerator: The desired outcome(s) Denominator: The total number of possibilities
Example: There are 4 blue marbles, 5 red marbles and 3 yellow marbles. If you randomly pull out one marble from the bag what is the probability it will be yellow?
If you have many similar events happening at the same time try using …
Probability Trees
Example: If you flip a coin 3 times what is the probability of getting 3 heads in a row?
3.2 NOTES Independent & Dependent Probability
Independent Events = ________________________________________
___________________________________________________________
Example: If you flip a coin 4 times what is the probability of getting 4 tails in a row?
What happens on a flip is not affected by the previous flips. Your turn! You spin the spinner shown to the right and flip a coin. Find the probability of each of the following: P(blue, heads) = ________ (*P means the probability of whatever is in the parentheses) P(green, tails) = ________ P(red OR yellow, tails) = _________ P(yellow AND blue, heads) = _________
Dependent Events = ________________________________________
__________________________________________________________
Example: There are 3 blue marbles and 7 red marbles in a bag. You randomly pull out one marble from the bag, leave it out, and then pull out another marble. What is the probability that both of the marbles you pull will be red?
What happens on the first pull affects what happens on the second pull.
Now you try!
Sample 1: You have a bag that contains 6 blue marbles, 3, red marbles, 4 orange marbles, and 2 green marbles. If you select a marble, DO NOT replace it, and then pick another, find the probability of each of the following scenarios:
P(blue, orange) = _________ P( green, green) = ________ P(red, blue) = _________ Sample 2: A deck of cards contains 52 cards made up of 4 suits (Diamonds, Hearts, Spades, Clubs). Each suit is made up of 13 cards (2 – Ace). If you were to pick a card from a deck, without replacing it, then pick another card, find the probability of each of the following: P(heart, club) = __________ P(diamond, diamond) = _____________
3.3 NOTES
Statistical Measures of Center
*REVIEW* What are the 3 Measures of Central Tendency?
______________________, ________________________ , ___________________
Definitions
Mean is found by _________________ all of the numbers and then _______________ by how many there are.
Median is the _________________ number, when they are ordered from least to greatest. **If there is no exact middle, you need to _________________________________________________.
Mode is the number that occurs the ________________________. ***There can be no mode, or many modes!
What’s the point of calculating these numbers????? By figuring out the measure of central tendency, you are choosing ONE number to __________________ the entire list of numbers.
Range shows the spread of the data (how spread out the numbers are on the list). It is found by finding the difference between the _________________ and ________________ numbers. ---------------------------------------------------------------------------------------------------------------------------------------
Let’s refresh ourselves with some examples with the data sets on the next page
A Data Set is the numbers that you have to work with. --------------------------------------------------------------------------------------------------------------------------------------- Which one is BEST for representing your data depends! Choose the … Mean: ____________________________________________________________________________________ __________________________________________________________________________________________ Median: __________________________________________________________________________________ __________________________________________________________________________________________ Mode: ____________________________________________________________________________________ __________________________________________________________________________________________
Sample # 1: 6, 3, 7, 12, 4, 3, 8
Order from least to greatest: _______, _______, _______, _______, _______, _______, _______, MEAN = __________ MEDIAN = __________ MODE = __________ RANGE = __________ --------------------------------------------------------------------------------------------------------------------------------------- Sample #2
27, 13, 42, 33, 13, 27, 48 Order from least to greatest: _______, _______, _______, _______, _______, _______, _______, MEAN = __________ MEDIAN = __________ MODE = __________ RANGE = __________ --------------------------------------------------------------------------------------------------------------------------------------- Sample #3
12, 8, 11, 17, 19, 11
Order from least to greatest: _______, _______, _______, _______, _______, _______, _______, MEAN = __________ MEDIAN = __________ MODE = __________ RANGE = __________
Mean Absolute Deviation: ____________________________________________________________________ ___________________________________________________________________________________________ The following table shows the age of 10 players on the Cardinals baseball team.
Age (in years)
Distance from
the Mean
Absolute Deviation
29 32 23 25 26 41 35 34 29 30
Mean = Mean Absolute Deviation=
Now let’s see how the heights of the students in our class are spread:
Student Height Distance from the Mean Absolute Deviation Mean Height = MAD =
3.4 NOTES Data Representation & Interpretation
Graphs are a great way to represent data in a visual manner.
Word Bank Intervals Frequency Title X-axis Labels Y-axis Time Range Bars BAR GRAPHS allow you to easily compare two or more things based on the ____________ (how often) they occur. This is why you need a ________________ table to create one.
All bar graphs must include the following things: 1) A ____________ 2) ____________ for the __________ and _________ 3) Steady and even ____________ between the numbers 4) __________ that do NOT touch
HISTOGRAMS are similar to bar graphs, but they show the frequency of data using a _______________ of data, instead of specific things. BAR GRAPHS vs. HISTOGRAMS
Similarities Differences _________________________________ ______________________________ _________________________________ ______________________________ _________________________________ ______________________________ LINE GRAPHS allow you to see how data changes over _____________. This is always located on the x-axis.
The ______________ is the horizontal axis (left to right)
The ______________ is the vertical axis (up and down)
STEM-AND-LEAF PLOTS are used to sort numerical data in order of place value. What does a stem-and-leaf plot show that no other type of graph shows? ____________________
Example: You went to the theater last Saturday and recorded the ages of all the people going to see a movie. You collected the following data:
15, 16, 14, 17, 19, 23, 21, 34, 31, 23, 26, 29, 30, 39, 37, 36, 18, 17, 21, 22, 55, 58 Step 1: Rearrange the numbers from least to greatest. Ages of Movie-Goers Step 2: Write all of the TENS places in the left-hand column (STEMS) Step 3: Write all of the ONES places (in order) in the same row as the tens place that belongs with it. (LEAVES) Do NOT use comas to separate leaves! Step 4: Don't forget to add a title and a key.
Key 3|1 = 31 years old SPECIAL NOTE: We still include the 40's stem since we have the 50's stem. We simply don't put anything in the leaf to show that no one was in their 40's. We would not put a zero since that would mean someone was 40.
Now you try ... (create a stem-and-leaf plot below)
Below are the percent scores on a test in Mr. Langford’s class:
98, 76, 88, 82, 79, 91, 90, 58, 72, 93, 95, 76, 88, 72, 100
For a DOUBLE Stem-and-Leaf Plot add the data for another class on the other side of the stem. The leaves go right to left! You will need to label each side and modify your key.
Below are the percent scores on a test in Mrs. Phillip’s class:
57, 75, 80, 80, 75, 91, 90, 58, 63, 92, 90, 55, 82, 70, 99
1 2 3 4 5
4 5 6 7 7 8 9 1 1 2 3 3 6 9 0 1 4 6 7 9 5 8
A BOX PLOT organizes data in QUARTILES. The quartiles are determined by finding the MEDIAN of the data at different points.
What does a box plot show that no other type of graph shows?
__________________________________________________________________________________________ __________________________________________________________________________________________ Example: To draw a box plot, we must first calculate some data points.
20, 11, 18, 25, 39, 29, 1
Step 1: Rearrange the numbers from least to greatest. 1, 11, 18, 20, 25, 29, 39 Step 2: Find the Median (M) The middle number is 20
Step 3: Find the Lower Quartile (LQ) and Upper Quartile (UQ)
*The LQ is the of the data below the Median. 1, 11, 18 … the LQ = 11
*The UQ is the of the data above the Median. 25, 29, 39 … the UQ = 29
Step 4: Find the Lower Extreme (LE) and Upper Extreme (UE)
*The LE is the number in the data set. The LE = 1 *The UE is the number in the data set. The UE = 39
Step 5: Draw a number line with evenly spaced intervals, starting at least one number below the lower extreme (LE) and at least one number above the upper extreme (UE).
Step 6: Place the LE, LQ, M, UQ, UE values as dots above OR below the number line.
Step 7: There are lines from LQ connected to the LE and the UQ connected to the UE. The box is made up of a rectangle using the LQ and the UQ as edge markers. The median is shown as the line cutting the box into two sections. Add a title and you have a box plot!
Temperatures in December
Now you try ... (create a box plot on the next page)
Draw a box plot for the percent scores on a math test.
99, 79, 86, 80, 87, 77, 94, 51 LE: __________ LQ: __________ M: __________ UQ: __________ UE: __________ Making Sense of Box Plots What fraction of the data is represented by each section of a box-and-whisker plot? ____________
What percent of the data is represented by each section of a box-and-whisker plot? ____________
What percent of the data is represented in the box section of a box-and-whisker plot? ___________
The range of the data in the box section is called the Inter-Quartile Range (IQR) [UQ – LQ]= ______
Price of Watches
If all of the watches under $45 are on sale, then what fraction of the watches are on sale?
A)
€
14
B)
€
12
C)
€
34
D) None of the above
**Why aren’t all the sections the same size?**
________________________________________________________________________________
________________________________________________________________________________
Make sense???? Try your hand at a DOUBLE box plot!
Average miles per gallon in city driving
What is the maximum miles per gallon for a sport utility vehicle? _____________ What is the IQR of the small cars? _________________
3.5 NOTES Population & Samples
Sampling is an important part of gathering information. Below are a few key words that we need to know:
Population: ________________________________________
_____________________________________________________________________________ Sample: _____________________________________________________________________
_____________________________________________________________________________
Here are some examples:
Population Sample Kirkwood School District Students Nipher Students
Cardinals Fans
Random Sample: _____________________________________________________________
____________________________________________________________________________ Representative Sample: ________________________________________________________
_____________________________________________________________________________ How could you collect a random sample? _________________________________________
_____________________________________________________________________________ *Question to ask: are all the elements of the population represented?
Samples: Biased vs. Unbiased I want to know the favorite team I want to know a favorite food I want to know _____________
3.6 NOTES Inferring, Surveying & Developing Statistical Questions
What does it mean to infer? ____________________________________________________
_____________________________________________________________________________ Example: The average height of fans in section 128 at a Chicago Bulls game is 5’11”. The average height of fans in section 128 at a Chicago Blackhawks game is 5’7”. What inferences can we make? Example: The average fan age at the last Rams game was 42.5 years. The average fan age at the last KHS Pioneer Varsity football game was 27.8 years. What inferences can we make? How can you write a good statistical question? Think back to our discussion about sampling. What info would help us here? Let’s list some elements of a good statistical question: ___________________________________________ _________________________________________________________________________________________ _________________________________________________________________________________________ Look at each of the following questions, and state whether you think it is a good statistical question or not. If not, think about what we could change to make it a good statistical question. 1) Do you like pets? 2) How old is your pet? 3) What percent of students in this school have pets? 4) What is the average height of students in this class? 5) Do you like pizza? 6) What is the favorite food of students in 7th grade? 7) How many rooms are in this school?
Why Did the Celebration
King's Birthday Last So Long?
Do each exercise and find your answer in the Code Key. Notice the letter under it. Write this letter in the box conta-ining the exercise number.
I. Find each probability if you spin the spinner once.
@) P(red) @ P(green)
@ P(blue or white) @) not yellow)
@ P(not red) @ P(blue or red or yellow)
II. Find each probability if you choose one card at ra-ndom.
@ P(striped)
@ P(shaded)
@ P(striped or white)
@ P(white)
@ P(white or shaded)
@ P(striped or shaded)
@ P(not striped) @ P(not white)
@ P(striped or white or shaded)
Ill. Solve.
@ What is the probability of guessing the correct answer to a multiple choice question if there are 5 choices?
@ What is the probability that your birthday will fall on Saturday or Sunday?
@ A class of 25 students has 15 girls and 10 boys. If one student is chosen at random, what is the probability it is a girl?
@ What is the probability of guessing the correct answer to a true-false question?
@ What is the probability of winning a raffle if 500 tickets are sold and you buy 5 of them?
@) There are 26 letters in the alphabet. What is the probability that a letter chosen at random is in the word MATHEMATICS?
MIDDLE SCHOOL MATH WITH PIZZAZZ! BOOK E 63 Creative Publications TOPIC 4-a: Probability
When the Boy Tire Maker Married the Girl Tire Maker, What Did Everyone Say?
Do each exercise and find your answer at the bottom of the page. Write the letter of the exercise in the box above the answer.
1. Suppose yo,u roll a regular 6-faced die.
@ How many equally likely outcomes are there?
@ If you roll the die once, what is the probability of rolling a 3?
@ If you roll the die 60 times, about how many times would you expect to get a 1
@ If you roll the die 300 times, about how many times would you expect to get a ....................................................... 2. A spinner is shown at the right for which each outcome is not equally likely.
@ If you spin the spinner once, what is the probability that it will stop on A?
@ If you spin the spinner once, what is the probability that it will stop on B?
@ If you spin the spinner 50 times, about how many times would you expect it to stop on A?
@ If you spin the spinner 80 times, about how many times would you expect it to stop on C?
3. Find each probability if you choose one marble at random.
@ P(black) @ P(striped)
@ P(not black) @ P(not white)
@ P(black or white) @ yellow)
4. Solve. ............................................................... @ If you flip a coin 150 times, about how @ If you randomly pick a date in April,
many times would you expect to get how many equally likely outcomes are heads? there?
@ The letters a, e, i, o, u, and y are @ A magician asks you to pick a card, vowels. If one letter of the alphabet is any card, from a standard deck of 52 chosen at random, what is the cards. What is the probability of probability it is a vowel? picking an ace?
TOPIC 4-b: Probability: Expected Outcomes MIDDLE SCHOOL MATH WITH PIZZAZZ! BOOK E
O Creative Publications
What Do the Police Put On a Bad Pig? Cross out the box containing each correct answer. (If an answer appears more than once, it doesn't matter which one you cross out.) When you finish, write the letters from the remaining boxes in the spaces at the bottom of the page.
I. Find each probability if you spin both spinners.
@ P(white, A) @ P(white, B)
@ P(striped, A) @ P(striped, B)
@ P(not striped, A) @ P(not striped, B)
@ P(not white, A) @ P(not white, B)
11. Find each probability if you spin the spinner and roll the number cube.
@ P(blue, 2) @ P(blue, not 2)
@ P( yellow, even) @ P(red, even)
@ P(not blue, 5) @ P(not blue, odd) 4 5 @ P(red, 4) @ P(red, not 4)
Ill. Find each probability if you pick one marble, replace it, then pick a second marble.
@ P(black, white) @ P(black, striped)
@ P(white, striped) @ P(not white, striped)
@ P(black, black) @ P(striped, striped)
@ P(white, not white) @ P(not white, not white)
IV. Solve.
@ A test has two multiple choice questions, each with five choices. What is the probability of guessing the correct answer to both questions?
@ One letter is randomly selected from the word MATH, and a second letter is randomly selected from the word JOKES. What is the probability that both letters are vowels?
TOPIC 4-d: Independent Events MIDDLE SCHOOL MATH WITH PIZZAZZ! BOOK E
O Creative Publications
% % % % - 8 % 3 - 12
- 7 - 9 , 1 0 , ~ , %
- - - - - - - - - -
- 1 5 %
- 8
A T T N O H E E A T P P I M G C O 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 4 4 5 6 7 8 8 9 1 0 e e % % % % % T H O U G S S L F A E E F A T S E 1 1 2 2 2 2 2 3 3 4 4 4 5 5 5 7 8 -
What Do You Get if a Bunch of Bad Guys Fall in the Ocean?
Cross out the box containing each correct answer. (If an answer appears more than once, it doesn't matter which one you cross out.) When you finish, write the letters from the remaining boxes in the spaces at the bottom of the page.
I. Find each probability if you pick a card, do not replace it, then pick a second card.
@ P(black, then white) @ P(black, then black)
@) P(white, then black) @ P(white, then white) ' II. Each letter of the word BANANA is written on a card. Find each probability if you pick two
cards without replacing the first.
@ P(B, then N) @ P(B, then A) @ P( N, then B)
@ P(N, then A) @ P(A, then 6) @ P(A, then N) Bmm
@ P(N, then N) @ P(A, then A) @ P(B, then B)
Ill. Find each probability if you pick a marble, do not replace it, then pick a second marble. (R = red; B = blue; G = green)
@ P(blue, then green) @ P(green, then red)
@ P(green, then green) @ P(green, then not green)
@ P(red, then blue) @ P(red, then not blue) '
@ P(blue, then blue) @ P(not blue, then not blue)
IV. Solve.
@ There were 6 purple socks and 4 @ There are 10 boxes in a grab bag. The orange socks in a drawer. Zucky picked boxes are identical except that 7 of one sock without looking and then them contain $20 bills. A contest winner another without looking (or replacing gets to pick two boxes from the grab the first). What is the probability that he bag. What is the probability of getting picked 2 purple socks? two $20 bills?
MIDDLE SCHOOL MATH WITH PIZZAZZ! BOOK E o Creative Publications Em53 TOPIC 4-e: Dependent Events
Name: ___________________________________________ Hr. ______
Measures of Central Tendency Investigation
Which one is the best? The following temperatures for a city were recorded during a week in June.
77, 76, 71, 70, 69, 70, 71
a) What is the mean temperature? ____________ Work:
b) What is the median temperature? ____________
c) What is the mode? ___________
d) What is the range? ___________
e) Which is the BEST measure of central tendency and why? ______________________ _____________________________________________________________________. *Another way to ask the question above: What average best represents the temperatures?
The number of home runs for some players on a baseball team are listed. 76, 11, 16, 17, 15, 12, 14, 9, 10
a) What is the mean number of home runs? __________ (show work)
b) What is the median number of home runs? _________ (show work)
c) What would be the mean if the highest number of home runs were removed? _________ (show work)
d) What is the mode? _________
e) What is the range? _________
f) Which is the BEST measure of central tendency and why? ______________________
_____________________________________________________________________.
Favorite Ice Cream Flavors Number of Votes
Chocolate 50 Vanilla 17
Strawberry 8
a) What is the mean? _________
b) What is the median? _________
c) What is the mode? _________
d) Which is the BEST measure of central tendency and why? ______________________ ______________________________________________________________________ ______________________________________________________________________.
Summary
1) What is an outlier? ________________________________________________________ _______________________________________________________________________.
2) When there is an outlier you use the _______________ as the best measure of central tendency.
3) When there is NOT an outlier you use the ________________ as the best measure of central tendency.
4) The ______________ is the best measure of central tendency when the data represents a vote OR you are trying to use a word to represent the data.
GRAPHING DATA
*Select one of the data sets below and create the best type of graph to display the data.
Total Pieces of Candy Received on Halloween (2015)
78, 29, 69, 37, 37, 73, 58, 37, 69, 48, 82, 27, 36, 37, 37, 73, 37, 54, 38
Heights of 1st Grade Students at Robinson Elementary
48, 42, 48, 36, 48, 46, 42, 48, 48, 46, 48, 48, 48, 46
Days of the Month in December 2014 on which a Football Game was Televised
2, 3, 7, 9, 11, 12, 14, 16, 17, 18, 22, 23, 24, 25, 30, 31
The Magnitudes of Earthquakes between 2012 and 2013
6.1, 6.6, 6.9, 6.3, 7.1, 6.4, 7.4, 5.8, 7.6, 4.6, 7.5, 5.9, 7.5, 5.3, 8.0, 5.1
Average Price of Organic Apples in Kirkwood
Year 2009 2010 2011 2012 2013 2014 Price $1.85 $2.10 $2.85 $3.65 $2.25 $2.75
Deceptive Statistics A look at how statistics can change how we look at situations
Example: Best Buy is having a sale on televisions. They are excitedly advertising that everyone can save $100 on all televisions! However, the small print excludes televisions under 50”. 50” televisions start at $800. Is this a great deal or not? Use statistics to support both sides. Show all work. Problem 1) Mr. Jones got a speeding ticket while travelling 25 mph in a 20 mph speed-limit zone. Mr. Jones argued to the judge that he shouldn’t have received the ticket, and that he was barely going over the speed limit. The police officer stated that the ticket was deserved, and that Mr. Jones shouldn’t just look at the amount he was over. Use statistics to support both sides. Show all work. Problem 2) Ms. Miller was so excited that her class averaged 82% on the last test. However, upon looking more closely at the individual scores, she wasn’t so sure that the 82% was an accurate representation of the overall class. Take a look at the scores below and find the Mean Absolute Deviation, to help determine how spread out the data really is, and if Ms. Miller’s hunch is correct. Show all work. Test Scores: 99, 65, 70, 62, 98, 92, 58, 100, 97, 79
Sampling the Population What is the average area & perimeter of a classroom at Nipher? What is the average height of students at Nipher? What is the average height of teachers at Nipher?
Drawing Conclusions & Making Inferences from Graphs Graph Conclusions/Inferences
Name __________________________ Date __________ Hour __________
3.6 Activity
You will conduct a survey to determine how many of the following texting shortcuts people know. In the survey you will try to determine whether teenagers or people over 30 know more of the shortcuts.
1. Write a questionnaire to use in your survey.
2. Determine the population and sample of your survey? Will your sample help to
determine what you are trying to?
Population:
Sample:
3. Conduct your survey. You must survey at least 30 people. Keep track of your data in an organized way (for example, make a table).
4. What inferences can you make from your results?
5. Do your results surprise you at all?
6. Was you sample biased or unbiased?
Name: ____________________________________ Date: _____________ Hr: ___________
Homework 3.1/3.2 Level 3
1) You roll a single six-sided die. What is the probability of each of the following? a) P(1) = ______ b) P(1 or 6) = ______ c) P(even #) = ______ d) P(not 4) = ______ e) P(odd #) = _____ f) P(not 2 or 3) = _____ g) P(even or odd) = _____ h) P(7) = _______
2) You randomly choose from five different cards (blue, red, orange, green and yellow). What is the probability expressed as a fraction, percent and decimal of choosing the blue card?
(A)
€
15,20%,0.02
(B)
€
15,50%,0.5
(C)
€
15,20%,0.2
(D) None of the above
3. Use the spinner to find the following probabilities. (Note: all sections are the same size) a) P(green) = ______ b) P(orange) = ______ c) P(yellow and blue) = _________ d) P(not red) = ________ e) P(green or yellow) = _______ 4. If you had no clue how to answer a multiple-choice question, and just randomly selected an answer from four options, what would be the probability of guessing correctly?
(A)
€
14
(B) 50%
(C)
€
0.3
(D) 1 in 5
5. A bag contains 2 yellow, 6 blue, 5 red, and 7 green marbles. If you reach in and select one marble, what is the probability that it will be blue? P(Blue) = _______
6. There are 26 letters in the alphabet. What is the probability that a letter chosen at random is in the word MATHEMATICS? P(MATHEMATICS) = ______
7. If you were to spin the spinner below 50 times, how many times would you expect to spin yellow? Yellow spins = _________
8. You flip a coin and roll a standard six-sided die. Make a Probability Tree to show all the possible outcomes. Total # of outcomes = _________
9. When getting dressed to go out, you have to decide between a red, blue, and green shirt, jeans or corduroys, and shoes or sneakers. Make a Probability Tree to show all ways you can put your outfit together. Total # of outcomes = _________
Name: ____________________________________ Date: _____________ Hr: ___________
Homework 3.1/3.2 Level 4
1) You roll a single six-sided die. What is the probability of each of the following? a) P(1) = ______ b) P(1 or 6) = ______ c) P(even #) = ______ d) P(not 4) = ______ e) P(odd #) = _____ f) P(not 2 or 3) = _____ g) P(even or odd) = _____ h) P(7) = _______
2) You randomly choose from five different cards (blue, red, orange, green and yellow). What is the probability expressed as a fraction, percent and decimal of choosing the blue card?
(A)
€
15,20%,0.02
(B)
€
15,50%,0.5
(C)
€
15,20%,0.2
(D) None of the above
3. Use the spinner to find the following probabilities. a) P(green) = ______ b) P(orange) = ______ c) P(yellow and blue) = _________ d) P(not red) = ________ e) P(green or yellow) = _______ 4. If you had no clue how to answer a multiple-choice question, and just randomly selected an answer from four options, what would be the probability of guessing correctly?
(A)
€
14
(B) 25%
(C) 0.25
(D) All of the above
5. A bag contains 3 yellow, 6 blue, 5 red, 7 green, and 9 orange marbles. If you reach in and select one marble, what is the probability that it will be blue? P(Blue) = _______
6. There are 26 letters in the alphabet. What is the probability that a letter chosen at random is in the word MATHEMATICS? P(MATHEMATICS) = ______
7. If you were to spin the spinner below 100 times, how many times would you expect to spin yellow (Y)? Yellow (Y) spins = _________
8. You flip a coin and roll a standard six-sided die. Make a Probability Tree to show all the possible outcomes. Total # of outcomes = _________
9. When getting dressed to go out, you have to decide between a red, blue, and green shirt, jeans or corduroys, and shoes or sneakers. Make a Probability Tree to show all ways you can put your outfit together. Total # of outcomes = _________
Name: ____________________________________ Date: _____________ Hr: ___________
Homework 3.2 Level 3
1. You flip a coin and roll a regular six-sided die at the same time. Find the probability of each of the following. (Show all work)
a) P(H, 1) = _________ b) P(T, even #) = __________ c) P(H, not 2) = _________
2. Find the following probabilities if you spin this spinner two times. (Show all work)
a) P(red, green) = _______ b) P(blue, blue)= ______ c) P(orange, not green) = _______
3. Find the probability of the following based on spinning both of these spinners at the same time. (Show all work)
a) P(A, 3) = _______
b) P(C, even) = _______
c) P(not B, odd) = _______
4. A bag contains 2 yellow, 5 blue and 3 red marbles. Find the following probabilities if you select one, replace it, and then select another. (Show all work)
a) P(blue, red) = _______ b) P(yellow, red) = _______ c) P(blue, not blue) = _______
5. A deck of cards contains 52 cards. There are 4 suits (hearts, diamonds, clubs, spades). Two suits are red (hearts, diamonds) and two are black (clubs, spades). You select a card, and then replace it in the deck before selecting the next card. Find the following probabilities. (Show all work) a) P(heart, club) = ______ b) P(red, spade) = ______ c) P(black, black) = _______
6. A bag contains 2 yellow, 5 blue and 3 red marbles. Find the following probabilities if you select one and then select another without replacing it. (Show all work)
a) P(yellow, blue) = _______ b) P(blue, red) = ______ c) (blue, not yellow) = ______
7. A deck of cards contains 52 cards. There are 4 suits (hearts, diamonds, clubs, spades). Two suits are red (hearts, diamonds) and two are black (clubs, spades). You select a card, and then without replacing it, you select another. Find the following probabilities. (Show all work) a) P(heart, club) = ______ b) P(red, spade) = ______ c) P(black, black) = _______
Name: ____________________________________ Date: _____________ Hr: ___________
Homework 3.2 Level 4
1. You flip a coin and roll a regular six-sided die at the same time. Find the probability of each of the following. (Show all work)
a) P(H, 1) = _________ b) P(T, even #) = __________ c) P(H, not 2) = _________
2. Find the following probabilities if you spin this spinner two times. (Show all work)
a) P(red, green) = _______ b) P(blue, blue)= ______ c) P(orange, not green) = _______
3. Find the probability of the following based on spinning both of these spinners at the same time. (Show all work)
a) P(A, 3) = _______
b) P(not C, even) = _______
c) P(B, not 2 or 5) = _______
4. A bag contains 2 yellow, 6 blue, 5 red, and 7 green marbles. Find the following probabilities if you select one, replace it, and then select another. (Show all work)
a) P(blue, green) = _______ b) P(yellow, red) = _______ c) P(blue, not blue) = _______
5. A deck of cards contains 52 cards. There are 4 suits (hearts, diamonds, clubs, spades). Two suits are red (hearts, diamonds) and two are black (clubs, spades). You select a card, and then replace it in the deck before selecting the next card. Find the following probabilities. (Show all work) a) P(heart, club) = ______ b) P(red, spade) = ______ c) P(black, black) = _______
6. A bag contains 2 yellow, 6 blue, 5 red, and 7 green marbles. Find the following probabilities if you select one and then select another without replacing it. (Show all work)
a) P(yellow, blue) = _______ b) P(green, red) = ______ c) (blue, not yellow) = ______
7. A deck of cards contains 52 cards. There are 4 suits (hearts, diamonds, clubs, spades). Two suits are red (hearts, diamonds) and two are black (clubs, spades). You select a card, and then without replacing it, you select another. Find the following probabilities. (Show all work) a) P(heart, club) = ______ b) P(red, spade) = ______ c) P(black, black) = _______
Name: ____________________________________ Date: _____________ Hr: ___________
3.3 Homework Level 3
1. Find the mean, median, mode(s), and range of the following data set. (Show all work)
12, 7, 37, 22, 22 Mean: _________
Median: ________
Mode: __________
Range: __________
2. Find the mean, median, mode(s), and range of the following data set. (Show all work)
2.1 , 3.2 , 4.7, 2.1, 1.9 Mean: _________
Median: ________
Mode: __________
Range: __________
3. This summer in St. Louis, the following temperatures were recorded over a 2 week period:
98, 101, 105, 103, 100, 99, 102, 102, 103, 99, 102, 100, 98, 102
Calculate the mean, median, mode(s) and range of the temperatures. (Show all work) Mean: _________
Median: ________
Mode: __________
Range: __________
4. Find the Mean Absolute Deviation of the temperatures in Problem #3 Temperature Deviation
frm the Mean Absolute Deviation
Mean= MAD=
5. Your health class tracked how many miles they ran for a week. Below are the results. What measure of central tendency would be best to interpret the data, and why?
3, 0, 1, 3, 62, 7, 5, 6, 3, 2, 4, 3
Mean Median Mode
Why? _______________________________________________________________________
____________________________________________________________________________
Name: ____________________________________ Date: _____________ Hr: ___________
3.3 Homework Level 4
1. Find the mean, median, mode(s), and range of the following data set. (Show all work)
2.1 , 3.2 , 4.7, 2.1, 1.9
Mean: _________
Median: ________
Mode: __________
Range: __________
2. You took a poll of students in your class about how many hours of homework they do each night. Below are the results. Calculate the mean, median and mode for the data.
2, 1, 3, 5, 3, 0, 5, 1, 3, 2, 3
Mean: ________
Median: ________
Mode: ________
Which measure best represents the data & why? ________________________________ _____________________________________
3. Which mean, median, mode and range below match the given data set?
98, 101, 105, 103, 100, 99, 102, 102, 103, 99, 102, 100, 98, 102
A) Mean: 101, Median, 101, Mode: 102, Range: 203 B) Mean: 1414, Median: 101.5, Mode: None, Range: 7 C) Mean: 101, Median: 101.5, Mode: 102, Range: 7 D) Mean: 101.5, Median: 101, Mode: 98, 99, 100, 102, 103, Range: 203
4. . Find the Mean Absolute Deviation of the temperatures in Problem #3 Temperature Deviation
frm the Mean Absolute Deviation
Mean= MAD=
5. Your Social Studies teacher had asked each student to write down the name of the candidate they would vote for in the election this November. What measure of central tendency would be best to interpret the results of the vote, and why?
Mean Median Mode Why? _______________________________________________________________________
____________________________________________________________________________
Name: ____________________________________ Date: _____________ Hr: ___________
3.4 Homework Level 3
1. The graph below shows the favorite sports of students on 6 North.
a) What sport do 6th grade boys like most? ________________________________________ b) What sport do Nipher students like most? ________________________________________
2.
a) Between which two years did City B (bottom line) have the smallest gain in population?
A) 1985-1990 B) 1990-1995
C) 1995-2000 D) 2000-2005
b) About how many people lived in City B in the year 2000?
A) 80 B) 72 C) 40 D) 80,000
3. Use the graph below to answer the questions to the right of the graph.
a) Between which two days was the consumption of potatoes the greatest?
A) Mon. and Tues. B) Tues. and Wed.
C) Wed. and Thur. D) Thur. and Fri.
b) How many kilos of potatoes are consumed in a week? ___________________________________ c) What is the average number of kilos of potatoes consumed in a day? ____________________________________
4. Create a double bar graph using the data below. Be sure to include a title, labels and a key.
Favorite Colors Survey Colors Blue Red Green Orange Yellow Boys 10 8 8 3 1 Girls 2 12 8 6 2
5. The prices of watches at a store are displayed in the box-and-whisker plot below.
a) What is the median price of a watch at this store? _________ b) How much is the most expensive watch at this store? _________ c) What is the Inter Quartile Range (IQR)? _________
Name: ____________________________________ Date: _____________ Hr: ___________
3.4 Homework Level 4
1. The graph below shows the favorite sports of students on 6 North.
a) What sport do 6th grade boys like most? ________________________________________ b) What sport do Nipher students like most? ________________________________________
2.
a) Between which two years did City B (bottom line) have the smallest gain in population?
A) 1985-1990 B) 1990-1995
C) 1995-2000 D) 2000-2005
b) About how many people lived in City B in the year 2000?
A) 80 B) 72 C) 40 D) 80,000
3. Use the graph below to answer the questions to the right of the graph.
a) Between which two days was the consumption of potatoes the greatest?
A) Mon. and Tues. B) Tues. and Wed.
C) Wed. and Thur. D) Thur. and Fri.
b) How many kilos of potatoes are consumed in a week? ___________________________________ c) What is the average number of kilos of potatoes consumed in a day? ____________________________________
4. Create a double bar graph using the data below. Be sure to include a title, labels and a key.
Favorite Colors Survey Colors Blue Red Green Orange Yellow Boys 10 8 8 3 1 Girls 2 12 8 6 2
5. The heights, in feet, of roller coasters in the United States are given below. Fill in the information below and create a box-and-whisker plot. (Show work)
35 80 45 48 100 52 83 42 76 47 LE = ______ LQ = ______ Median = ______ UQ = ______ UE = ______
a) What is the median height of roller coasters? _________ b) How much is the highest roller coaster? _________ c) What is the Inter Quartile Range (IQR)? _________
Name ____________________________________ Date __________ Hour _________
3.5 Homework 1. An agency wants to know the opinions of Missouri residents on the construction of a new road. The agency surveys 800 residents. Identify the population and the sample. Population: Sample:
2. Identify the population and the sample. Population: Sample:
3. You want to know the number of students in your school who play a musical instrument. You survey the first 15 students who arrive at a band class. a. What is the population of your survey?
b. Is the sample biased or unbiased? Why?
4. If you want to know the average height of seventh graders in St. Louis would you survey the population or the sample? Explain.
5. In a classroom of 30 students where half of the students are male and half are female give an example of a representative sample.
6. Give an example of a random sample. How would you collect this random sample?
7. If the population is all Kirkwood School District students name three possible samples: 1 _________________________________ _________________________________ 2 _________________________________ _________________________________ 3 _________________________________ _________________________________
8. What is an example of a survey you could give to one of your samples from problem #7. Is your survey biased, or not biased? Explain.
9. Which sample is better for making a prediction? To predict the number of students in a school who like gym class. Sample A: a random sample of 8 students from the yearbook. Sample B: a random sample of 80 students from the yearbook. Explain your choice below.
10. . Which sample is better for making a prediction? To predict the number of defected pencils produced per day. Sample A: a random sample of 500 pencils from 20 different pencil machines. Sample B: a random sample of 500 pencils from the same pencil machine. Explain your choice below.
Name: _________________________________ Date: __________ Hr: ________
Unit 3 Review
3.1 - Introduction to Probability and Probability Trees Score _____
3.2 - Independent and Dependent Probability Score _____ 3.3 - Statistical Measures of Center Score _____
3.4 - Data Representations Score _____
3.1/3.2 Introduction to Probability & Probability Trees/Independent Probability - Type 2 1. You roll a single six-sided die. What is the probability of each of the following? a) P(3) = ________ b) P(odd) = __________ c) P(not 6) = _________
2. Your teacher has a bag with 2 blue tickets, 3 red tickets and 1 white ticket in it. What is the probability that you pick a blue ticket?
(A)
€
13
(B) 33% (C)
€
0.3 (D) All of the above (E) None of the above
3.1/3.2 Introduction to Probability & Probability Trees/Independent Probability Type 3
3. Make a probability tree to show all the possible outcomes for combining black or grey pants with a white or blue shirt and a blue, red or black tie.
4. You spin the spinner below. Find each of the following probabilities.
a) P(yellow) = ________
b) P(orange) = ________
c) P(red or green) = ________
d) P(not blue) = ________
3.2 – Dependent Probability
Type 2 5. You flip a coin and roll a single six-sided die at the same time. Find each of the probabilities. (Show all work) a) P(H, 3) = _________ b) P(T, odd #) = ________ c) P(H, not 5) = ____________
6. You spin the spinner below twice. Find each of the following probabilities. (Show all work) a) P(red, yellow) = _______ b) P(green, green) = ______ c) P(blue, not orange) = ________
3.2 – Dependent Probability
Type 3 7. There are 26 letters in the alphabet. Each of them is on a card in a bag. Find each of the following probabilities, if you select a letter, replace it, and then select again. a) P(A, Z) = ________ b) P(vowel, L) = _________ c) P(consonant, consonant) = __________
8. There are 26 letters in the alphabet. Each of them is on a card in a bag. Find each of the following probabilities, if you select a letter, DO NOT replace it, and then select again. a) P(A, L) = __________ b) P(vowel, M) = ________ c) P(vowel, consonant) = _______
3.3 - Statistical Measures of Center - Type 2
9. Find the mean, median, mode(s), and range of the following data set. (Show all work)
12.3, 8.8, 9.6, 11, 9.5, 11.8 Mean: _________
Median: ________
Mode: __________
Range: __________
10. Your cross-country team ran the following times (in min) in the most recent race. Calculate the mean, median, mode and range.
20.55, 19.85, 44.35, 22.19, 20.2, 21.98, 21.55
Mean: _________ Median: ________
Mode: _________ Range: _________
Which measure best represents the data set and why?
Mean Median Mode Range
Why?________________________________ _____________________________________ _____________________________________
3.3 - Statistical Measures of Center - Type 3
11. Use the information & data set from Problem #10 to find the Mean Absolute Deviation of the times of the cross-country runners.
Time (in min)
Deviation from Mean
Absolute Deviation
Mean = MAD=
12. Describe a scenario where using MEAN would be the best way to represent the data. Use at least 6 numbers in your data set. Scenario: _____________________________________
_____________________________________
_____________________________________
_____________________________________
_____________________________________ Numbers: ___ , ___ , ___ , ___ , ___ , ___
3.4 - Data Representations Type 2 13. a) What inferences can you make from this graph? (Write at least 2) _____________________________________ _____________________________________
14. a) How many cars were sold from April to September?
_____________________________________ b) Predict about how many cars would be sold in all of 2012?
_____________________________________
3.4 - Data Representations - Type 2 & 3 15. The box-and whisker plot to the English Test Scores right shows the most recent English test scores for a HS class.
a) What was the best score on the test? _________
b) What is the median score? _______
c) What is the IQR of the scores? ______
16. The points scored over seven games are given below. Create a box-and-whisker plot below of the data. Football Points: 7 10 14 14 21 24 28
Fill in the information below.
LE = ______ LQ = ______ Median = ______ UQ = ______ UE = ______ Create a box-and-whisker plot below.
What is the IQR of the points? ______
3.4 - Data Representations Type 3 17. Below are the amounts of Box Tops collected by the Nipher teams during the 2016-2017 school year.
6 North: 255 6 South: 275 7 North: 305 7 South: 237 8 North: 212 8 South: 280
a) Which type of graph would be best to display the data above? (circle one) Bar Graph Histogram b) Create the graph below. c) If someone asked you “how many box tops did a team at Nipher collect?” What would be your answer? Why? _______________________________________________________________________ _____________________________________________________________________________ _____________________________________________________________________________
