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Chapter 4: Collecting, Displaying, and Analyzing Data. Regular Math. Section 4.1: Samples and Surveys. Population – the entire group being studied Sample – part of the population Biased Sample – not a good representation Random Sample – every member has an equal chance - PowerPoint PPT Presentation
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Chapter 4: Collecting, Displaying, and Analyzing Data
Regular Math
Section 4.1: Samples and Surveys Population – the entire group being studied
Sample – part of the population
Biased Sample – not a good representation
Random Sample – every member has an equal chance
Systematic Sample – according to a rule or formula
Stratified Sample – at random from a randomly subgroup
Example 1: Identifying Biased Samples Identify the population and sample. Give a reason why the sample could
be biased. A radio station manager chooses 1500 people from the local phone book to
survey about their listening habits. Population = people in the local area Sample = up to 1500 people that take the survey Biased = not everyone is in the phone book
An advice columnist asks her readers to write in with their opinions about how to hang the toilet paper on the roll. Population = readers of the column Sample = readers who wrote in Biased = only readers with strong opinions would write in
Surveyors in a mall choose shoppers to ask about their product preferences. Population = all shoppers at the mall Sample = people who are polled Biased = surveyors are more likely to approach people who look agreeable
Try these on your own… Identify the population and sample. Give a reason why
the sample could be biased. A record store manager asks customers who make a
purchase how many hours of music they listen to each day. Population = record store customers Sample = customers who make a purchase Biased = Customers who make a purchase may be more
interested in music than others who are in the store. An eighth-grade student council member polls classmates
about a new school mascot. Population = students in the school Sample = classmates Biased = She polls more eighth graders than students in other
grades.
Sampling Method How Members Are Chosen
Random By chance
Systematic According to a rule or formula
Stratified At random from randomly chosen subgroups
Example 2: Identifying Sampling Methods Identify the sampling method used.
An exit poll is taken of every tenth voter. systematic
In a statewide survey, five counties are randomly chosen and 100 people are randomly chosen from each county. stratified
Students in a class write their names on strips of paper and put them in a hat. The teacher draws five names. random
Try these on your own…
Identify the sampling method used. In a county survey, Democratic Party members whose
names begin with the letter D are chosen. systematic
A telephone company randomly chooses customers to survey about its service. random
A high school randomly chooses three classes from each grade and then draws three random names from each class to poll about lunch menus. stratified
Section 4.2: Organizing Data
Stem-and-Leaf Plot
Back –to-Back Stem-and-Leaf Plot
Example 1: Organizing Data in Tables Use the given data to make
a table. Greg has received job
offers as a mechanic at three airlines. The first has a salary range of $20,000-$34,000, benefits worth $12,000, and 10 days’ vacation. The second has 15 days’ vacation, benefits worth $10,500, and salary range of $18,000-$50,000. The third has benefits worth $11,400, a salary range of $14,000-$40,000, and 12 days’ vacation.
Job 1 Job 2 Job 3
Salary Range
$20,000 -
$34,000
$18,000-
$50,000
$14,000-
$40,000
Benefits
$12,000 $10,500 $11,400
Vacation Days
10 15 12
Try this one on your own…
Day To School To Home
Monday 7 min 9 min
Tuesday 5 min 9 min
Wednesday 8 min 7 min
Use the given data to make a table. Jack timed his bus rides
to and from school. On Monday, it took 7 minutes to get to school and 9 minutes to get home. On Tuesday, it took 5 minutes and 9 minutes respectively, and on Wednesday, it took 8 minutes and 7 minutes.
Example 2: Reading Stem-and-Leaf Plots List the data values in
the stem-and-leaf plot.
0 2 5
1 3 3 7 8
2 0 2 6
3 1 7
Key: 3 I 1 means 31
Try this one on your own…
1 2 5
2 0 1 1
3 2 7 9
12, 15, 40, 41, 41, 52, 57, 59
Example 3: Organizing Data in Stem-and-Leaf PlotsAsh 47 Elm 38 Red Maple 55
Beech 40 Grand Fir 77 Sequoia 84
Black Maple 40 Hemlock 74 Spruce 63
Cedar 67 Hickory 58 Sycamore 40
Cherry 42 Oak 61 Western Pine 48
Douglas Fir 91 Pecan 44 Willow 35
Use the data set on heights of trees in the U.S. (m) to make a stem-and-leaf plot.
Try this one on your own…
Use the data on top speeds of animals (mi/h) to make a stem-and-leaf plot.
Cheetah 64 Elk 45
Wildebeest 61 Coyote 43
Lion 50 Gray Fox 42
Example 4: Organizing Data in Back-to-Back Stem-and-Leaf Plots Use the given data on Super Bowl scores, 1990-
2000, to make a back-to-back stem-and-leaf plot.
1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000
Winning 55 20 37 52 30 49 27 35 31 34 23
Losing 10 19 24 17 13 26 17 21 24 19 16
Try this one on your own…
Use the data on US. Representatives for Selected States, 1950 and 2000, to make a back-to-back stem-and-leaf plot.
IL MA MI NY PA
1950 25 14 18 43 31
2000 19 10 15 29 19
Section 4.3: Measures of Central Tendency
Definition Use to Answer
Mean – the sum of the values, divided by the number of values
“What is the average?”
“What single number best represents the data?”
Median – the middle number in an ordered set of data
“What is the halfway point of the data?”
Mode – the value or values that occur most often
“What is the most common value?”
Section 4.4: Variability
Variability – how spread out the data is
Range – largest number minus the smaller number
Quartile – divide data parts into four equal parts
Box-and-Whisker Plot – shows the distribution of data
Example 1: Finding Measures of Variability Find the range and the first and third quartiles
for each data set. 85, 92, 78, 88, 90, 88, 89
78, 85, 88, 88, 89, 90, 92 Range: 92-78 = 14 1st Quartile = 85 3rd Quartile = 90
14, 12, 15, 17, 15, 16, 17, 18, 15, 19, 20, 17 12, 14, 15, 15, 15, 16, 17, 17, 17, 18, 19, 20 Range: 20-12 = 8 1st Quartile = (15 + 15) / 2 = 15 3rd Quartile = (17 + 18) / 2 = 17.5
Try these on your own…
Find the range and the first and third quartiles for each data set. 15, 83, 75, 12, 19, 74,
21
Range: 71 1st Quartile: 15 3rd Quartile: 75
75, 61, 88, 79, 79, 99, 62, 77
Range: 38 1st Quartile: 69 3rd Quartile: 83.5
Example 2: Making a Box-and-Whisker Plot Use the given data to make a box-and-
whisker plot. 22, 17, 22, 49, 55, 21, 49, 62, 21, 16, 18, 44, 42,
48, 40, 33, 45 Find the smallest value, first quartile, median, third
quartile, and largest value. Smallest: 16 1st Quartile: (21+21) / 2 = 21 Median: 40 3rd Quartile: (48+49) / 2 = 48.5 Largest: 62
Try this one on your own…
Use the given data to make a box-and-whisker plot. 21, 25, 15, 13, 17, 19, 19, 21
Smallest: 13 1st Quartile: 16 Median: 18 3rd Quartile: 21 Largest: 25
Example 3: Comparing Data Sets Using Box-and-Whisker Plots These box-and-whisker
plots compare the number of home runs Babe Ruth hit during his 15-year career from 1920 to 1934 with the number Mark McGwire hit during the 15 years from 1986 to 2000.
Compare the medians and ranges.
Compare the ranges of the middle half of the data for each.
Try these on your own…
These box-and-whisker plots compare the ages of the first ten U.S. presidents with the ages of the last ten presidents (through George W. Bush) when they took office.
Compare the medians and ranges.
Compare the differences between the third quartile and first quartile for each.
Section 4.5: Displaying Data
Bar Graph – display data that can be grouped in categories
Frequency Table – use with data that is given in list
Histogram – type of bar graph; groups by using intervals
Line Graph – show trends or to make estimates
Example 1: Displaying Data in a Bar Graph Organize the data into
a frequency table and make a bar graph.
The following are the ages when a randomly chosen group of 20 teenagers received their driver’s licenses: 18, 17, 16, 16, 17, 16, 16, 16, 19, 16, 16, 17, 16, 17, 18, 16, 18, 16, 19, 16
Age License
Received
16 17 18 19
Frequency 11 4 3 2
Try this one on your own…
Organize the data into a frequency table and a bar graph.
The following data set reflects the number of hours of television watched every day by members of a sixth-grade class: 1,1,3,0,2,0,5,3,1,3
Hours Frequency
0 2
1 3
2 1
3 3
4 0
5 1
Example 2: Displaying Data in a Histogram John surveyed 15 people
to find out how many pages were in the last book they read. Use the data to make a histogram. 368, 153, 27, 187, 240, 636,
98, 114, 64, 212, 302, 144, 76, 195, 200
Make a frequency table first.
Then, use intervals of 100 to make a histogram.
Pages Frequency
0-99
100-199
200-299
300-399
400-499
500-599
600-699
Try this one on your own…
Dollars Frequency
0-0.99
1.00 – 1.99
2.00 – 2.99
3.00 – 3.99
Jimmy surveyed 12 children to find out how much money they received from the tooth fairy. Use the data set to make a histogram. 0.35, 2.00, 0.75, 2.50,
1.50, 3.00, 0.25, 1.00, 1.00, 3.50, 0.50, 3.00
Example 3: Displaying Data in a Line Graph Make a line graph of
the given data.
Use the graph to estimate the number of polio cases in 1993.
Year Number of Polio Cases
Worldwide
1975 49,293
1980 52,552
1985 38,637
1990 23,484
1995 7,035
2000 2,880
Try this one on your own…
Year Salary ($)
1985 42,000
1990 49,000
1995 58,000
2000 69,000
Make a line graph of the given data.
Use the graph to estimate Mr. Yi’s salary in 1992.
Section 4.6: Misleading Graphs and StatisticsExplain why each graph is misleading.
Try this one on your own…
Explain why the graphs are misleading.
Example 2: Identifying Misleading Statistics Explain why each statistic is misleading.
A small business has 5 employees with the following salaries: $90,000 (owner); $18,000; $22,000; $20,000; $23,000. The owner places an ad that reads: “Help Wanted – average salary $34,600” Only one person in the company makes more than $23,000 and that is the owner.
It is not likely that a new person’s salary would be close to $34,600. A market researcher randomly selects 8 people to focus-test three
brands, labeled A, B, and C. Of these, 4 chose brand A, 2 chose brand B, and 2 chose brand C. An ad for brand A states: Preferred 2 to 1 over leading brands!” The sample size is too small. The researcher needs to ask more people to get a
true representation. The total revenue at Worthman’s for the three-month period from June 1
to September 1 was $72,000. The total revenue at Meilleure for the three-month period from October 1 to January 1 was $108,000. They are comparing two different times of the year.
Try these on your own…
Explain why each statistic is misleading. Sam scored 43 goals for his soccer team during
the season, and Jacob scored only 2.
Four out of five dentists surveyed preferred Ultraclean toothpaste.
Shopping at Save-a-Lot can save you up to $100 a month!
Section 4.7: Scatter Plots
Scatter Plots – show relationships between two data sets
Example 1: Making a Scatter Plot of a Data Set
Compound ZIA Average Effects
Zinc Gluconate 100 Reduced cold 7 days
Zinc Gluconate 44 Reduced cold 4.8 days
Zinc Orotate 0 None
Zinc Gluconate 25 Reduced cold 1.6 days
Zinc Gluconate 13.4 None
Zinc Aspartate 0 None
Zinc Acetate-tartarate-glycine -55 Increased cold 4.4 days
Zinc Gluconate -11 Increased cold 1 day
A scientist studying the effects of zinc lozenges on colds has gathered the following data. Zinc ion availability (ZIA) is a measure of the strength of the lozenge. Use the data to make a scatter plot.
Try this one on your own…
Use the given data to make a scatter plot of the weight and height of each member of a basketball team.
Height (in) Weight (lb)
71 170
68 160
70 175
73 180
74 190
Correlations
Example 2: Identifying the Correlation of Data Do the data sets have positive, a negative, or
no correlation? The population of a state and the number of
representatives positive
The number of weeks a movie has been out and weekly attendance negative
A person’s age and the number of siblings they have No correlation
Try these on your own…
Do the data sets have a positive, negative, or no correlation? The size of a jar of baby food and the number of
jars a baby eats negative
The speed of a runner and the number of races she wins positive
The size of a person and the number of fingers he has No correlation
Example 3: Using a Scatter Plot to Make Predictions
Use the data to predict the exam grade for a student who studies 10 hours per week.
About 95
Hours Studied Exam Grade
5 80
9 95
3 75
12 98
1 70
Try this one on your own…
Use the date to predict how much a worker will earn in tips in 10 hours.
Approximately $24
Hours Tips ($)
4 12
8 20
3 7
2 7
11 26