Algebra II: Chapter 12 Probability and Statistics Section

Algebra II: Chapter 12 Probability and Statistics

Section P.1: Mean, Median, and Mode

Mean, Median, and Mode are measures of ________________________________________ that are often used

to represent a set of __________________.

1) The mean is often called the _________________________. To find the mean, find the ___________ of

the data and then ___________________ by the number of items in the data set.

2) The median is the ___________________________________ of the data. To find the median, you must

ARRANGE the data from _____________________________ to ______________________________.

The median is middle number after the data has been ordered. If there is an even number of data, the

median is the ________________ of the two middle numbers.

3) The mode is the number (or numbers) that ______________________ the most often in a set of data. If

no item appears most often, the set has ________________________.

Ex. 1: Michelle is saving to buy a car. She saved $200 in June, $300 in July, $400 in August, and $150 in

September. What was her mean monthly savings?

Ex. 2: Find the median of Peter’s running times.

Ex. 3:

The range of a set of data is the ____________________________________ between the _________________

and the ____________________________ values of the set.

Ex. 4: Find the range of the data. {6, 11, 18, 4, 9, 15, 6, 3}

Ex. 5: Find the mean, median, mode, and range for the set of data. {2, 8, 12, 13, 15}

Ex. 6:

Ex. 7: Kaitlyn’s scores on her first five algebra tests are 88, 90, 91, 89, and 92. What test score must Kaitlyn

earn on the sixth test so that her mean score will be at least 90?

HW: 1) Find the mean, median, mode, and range for each set of data.

{6, 12, 21, 43, 1, 3, 13, 8}

2)

3)

4) Colin’s average for three rounds of golf is 94. What is the highest score he can receive for the fourth round to

have an average (mean) of 92?

5) To earn a grade of B in math, Latisha must have an average (mean) score of at least 84 on five math tests.

Her scores on the first three tests are 85, 89, and 82. What is the lowest total score that Latisha must have on the

last two tests to earn a B test average?

P. 2: Bar and Line Graphs and Stem-and-Leaf Plots

A _________________________ compares different categories of data by showing each as a bar whose

__________________ is related to the __________________________. A ____________________ bar graph

compares two sets of data. Another way to represent data is by using a ________________________. A line

graph usually shows how data _______________________ over a period of time.

Ex. 1:

Ex. 2:

In a _____________________________, data are organized in two columns. The greatest plave value of the

data is used for the stems. The next greatest place value forms the leaves. Stem-and-leaf plots are useful for

_____________________________ long lists of numbers.

Ex. 3:

Ex. 4:

HW:

3.

4.

P. 3: Box-and-Whisker Plots

In a set of data, ________________________ are values that divide the data into four equal parts.

To make a box-and-whisker plot, draw a box around the _______________________ values, and lines or

whiskers to represent the values in the ____________________________ of the data and the _______________

of the data.

Ex. 1:

The _________________________________________________ is the range of the middle half of the data and

contains 50% of the data in the set.

IQR = _____________________________________

An ____________________________ is any element of a set that is at least _________ IQRs less than the

lower quartile or greater than the upper quartile. The _______________________ representing the data is

drawn from the box to the least or greatest value that is not an outlier.

Ex. 2:

a. What percent of the data lies between 1.5 and 3.25?

b. What was the greatest amount of time Jose’ studied in a day?

c. What is the interquartile range of this box-and-whisker plot?

d. Identify any outliers in the data?

HW:

1) What percent of the students drive more than 30 miles in a day?

2) What is the interquartile range of the box-and-whisker plot?

3) Does a student at Tyler’s school have a better chance to meet someone who drives the same mileage

they do if they drive 50 miles in a day or 15 miles in a day? Why?

4)

5)


Section 12-1: The Counting Principle

Question: How many different license plates are possible in the state of Pennsylvania?

An ________________ is the result of a single trial. Ex. _________________________ has two outcomes:

_______________ or ________________. The set of all possible outcomes is called the _______________

_______________. An __________________ consists of one or more outcomes of a trial. When one event does

NOT affect the choices for a second event, the events are said to be __________________________.

One way to count the number of possible outcomes of multiple events is to use a _____________________.

Ex. 1: A sandwich cart offers customers a choice of hamburger, chicken, or fish on either a plain or a sesame

seed bun. How many different combinations of mean and a bun are possible?

Notice that there are _______ ways to choose the type of meat, ________ ways to choose they of bun, and

___________ total way to choose a combination of the two. This is an example of the

__________________________________________________________________________________.

Ex. 2:

The Funadamental Counting Principle can be used to count the number of outcomes possible for any number of

successive events.

Ex. 3:

_________________________ Events: Some situations involve dependent events. With dependent events, the

outcome of one event _____________ affect the otucome of another event. The Fundamental Counting

Principle _________________________ to Dependent events as well as Independent Events.

Ex. 4:

HW: 1) State whether the events are independent or dependent.

a.

b.

c.

d.

2) Solve the following problems:

a.

b.

c.

d.


Section 12-2: Permutations and Combinations

When a group of objects or people are arranged in a certain order, the arrangement is called a

_________________________. In a permutation, the ____________________ of the objects is very important.

To evaluate permutations, use the ________________________________!!!!!

Ex. 1: Evaluate P(7, 7).

Ex. 2: Evaluate P(7, 4).

Ex. 3:

When solving permutations with repetitions use the following formula:

Ex. 2:

Ex. 3: How many different ways can the letters in the word geometry be arranged?

When order does not matter: an arrangement of objects in which order is NOT important is called a

_____________________________. The number of combinations of n objects taken r at a time is written

C(n, r).

Ex. 4:

Ex. 5:

HW: 1)

2)

3)

4)

5)

a.

b

c.

d.

e.

f.

g

h


Section 12-3: Probability

The ________________________ of an event is a _______________ that measures the chance of the event

occurring.

A desired outcome is called a ____________________. Any other outcome is called a ___________________.

*** The probability of an event occurring is always between _____ and _____.

Ex. 1: When two coins are tossed, what is the probability that both are tails?

When all outcomes are equally likely, we say that the outcomes occur at _____________________.

Ex. 2:

Another way to measure the chances of an event occurring are with ______________. The ____________ that

an event will occur can be expressed as the ____________________ of the number of ____________________

to the number of ____________________________________.

Ex. 3:

HW: 1) 2) a. b. c.

f. d. e. g. h.

a. b. c.


Section 12-4: Multiplying Probability

Recall: Two events are said to be ________________________________ if the outcome of one event does not affect the probability of the outcome of another event. Examples of independent events: flipping a coin, rolling dice, spinning spinners. If we want to find the probability of multiple independent events, we ________________________________ the probabilities of each event.

________________________________ Events – when the occurrence of one event DOES change the probability of the second event occurring. Examples of dependent events: drawing cards from a deck without replacement, or drawing marbles from a bag without replacement.

HW: 1) a. b. c. d. e. f. 2)

a.

b.

c.

d.


Section 12-5: Adding Probability

Events that cannot happen at the same time are called _____________________________________ events.

Examples of mutually exclusive events: drawing an Ace or a Queen.

Inclusive Events – when two events could happen at the same time, we call the events mutually ____________.

Example of mutually inclusive: Drawing a spade or a queen.

HW: 1)

a. b. c.

2) Determine whether the events are mutually exclusive or mutually inclusive and then determine the

probability of each event.

a.

b.

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Algebra II: Chapter 12 Probability and Statistics Section