19. central tendency and variability

Central Tendency and Variability

1. Mrs. Higgins' Home Economics class collected data on the number of chocolate chips in

cookies for two different brands, as shown in the dot plots below.

The mean absolute deviation for each brand is 0.8. The difference between the mean number of

chocolate chips for each brand is approximately how many times the mean absolute deviation?

A. 7

B. 3

C. 6

D. 5

2. A health researcher conducted a survey and recorded the percentage of body fat of 20

randomly selected men from two different towns. Ten of the men surveyed were from Pythagoria

and 10 of the men were from Bernoullia. The following statistical information was calculated

from the researcher's findings.

Pythagoria

Bernoullia

First Quartile 12 15

Second Quartile (Median) 16 19.5

Third Quartile 19 25

Based on these samples, what generalization can be made?

A. Pythagoria has men with higher body fat percentages than Bernoullia.

B. The interquartile range of body fat percentages for Pythagoria is less than Bernoullia.

C. Not enough information is provided to draw any of these conclusions.

D. At least half of the men from both towns have between 10 and 20 percent body fat.

3. A health researcher conducted a survey and recorded the percentage of body fat of 20

randomly selected men from two different towns. Ten of the men surveyed were from Pythagoria

and 10 of the men were from Bernoullia. The following statistical information was calculated

from the researcher's findings.

Pythagoria

Bernoullia





A. Not enough information is provided to draw any of these conclusions.

B. At least half of the men from both towns have between 10 and 20 percent body fat.

C. The interquartile range of body fat percentages for Pythagoria is less than Bernoullia.

D. Pythagoria has men with higher body fat percentages than Bernoullia.

4. At a certain company, the sales records of 30 employees were examined. Fifteen of the

employees were married and 15 of them were not married. The following statistical information

was calculated from the number of sales of each employee chosen.

Married

Unmarried

Mean 113 97

Median 103 105

Mode 94 105

Range 80 84


A. The married employees sold more units than the unmarried employees.

B. The married employees sold the same number of units as the unmarried employees.

C. The unmarried employees sold more units than the married employees.

D. Not enough information is provided to draw any of these conclusions.

5. The dot plots below show the number of apples in 5-pound bags at two different stores.

The variability at each store is 1.6. The difference between the mean number of apples per bag at

each store is approximately how many times the variability?

A. 4

B. 2

C. 3

D. 5

6. At a car dealership, the sales records of weekdays and weekends were examined. Ten of the

days examined were weekdays and 10 of them were weekend days. The following statistical

information was calculated from the number of sales made during weekdays and weekends.

Weekday

Sales

Weekend

Sales

Mean 15 18

Median 13 19

Mode 14 21

Range 10 13



B. More cars were sold on the weekdays than on the weekends.

C. The same number of cars were sold on the weekends as on the weekdays.

D. Less cars were sold on the weekdays than on the weekends.

7. A wildlife biologist catches and releases 20 fish from two different lakes at random locations.

He catches 10 fish at Lake Palmer and 10 fish at Lake Dalton. He measures the length of each

fish to the nearest quarter of an inch.

Palmer

Dalton

First Quartile 6.75 5.5

Second Quartile (Median) 10.25 6.75

Third Quartile 13 7.5

Based on the samples, what generalization can be made?


B. The interquartile range for Lake Dalton is 2 inches greater than the interquartile range

for Lake Palmer.

C. The first quartile value at Lake Palmer is 1.25 inches longer than the first quartile value

at Lake Dalton.

D. At least 25 percent of the fish in both lakes are no longer than 6 inches.

8. A forester measured the diameter of 20 randomly selected pine trees from two different forests

in inches. He measured the diameter of 10 trees in Pebble Brook forest and 10 trees in Piney

Woods forest. He then calculated the following statistical information.

Pebble Brook

Piney Woods





A. The third quartile of diameters is greater for the trees in Pebble Brook than in Piney

Woods.

B. The first quartile of diameters is less for the trees in Pebble Brook than in Piney Woods.

C. The median of diameters is greater for the trees in Piney Woods than in Pebble Brook.

D. The interquartile range of diameters is greater for the trees in Piney Woods than in

Pebble Brook.

9. The dot plots below show the prices of used cars sold in one month at two competing car

dealerships.

The variability at each dealership is approximately 1.538 hundred dollars. The difference

between the mean price of used cars sold at each dealership is approximately how many times

the variability?

A. 9

B. 4

C. 5

D. 6

10. Sammy conducted an experiment which consisted of spinning two spinners. Spinner 1 had

sections numbered 8 to 14, and spinner 2 had sections numbered 1 to 7. The results are recorded

in the dot plots below.

The mean absolute deviation for each spinner is 1.75. The difference between the median result

for each spinner is how many times the mean absolute deviation?

A. 4

B. 3

C. 5

D. 2

11. The dot plots below show the numbers sold of a new menu item at two restaurant locations

each day in June.

The variability at each restaurant location is 1.76. The difference between the mode number of

new menu items sold per day at each location is approximately how many times the variability?

A. 6

B. 7

C. 5

D. 4

12. A government agency conducted energy research on two different towns. The agency

selected 12 homes from each town and recorded the number of kilowatt-hours used by the homes

over a one-year period. The following statistical information was calculated from their findings.

Jacobia

Cantorville

Mean 11,178 11,613

Median 11,653 11,572

Mode 11,705 11,050

Range 2,137 2,188


A. Jacobia used more kilowatt-hours than Cantorville.

B. Both towns used the same number of kilowatt-hours.


D. Cantorville used more kilowatt-hours than Jacobia.

13. The dot plot below shows the average fuel efficiency of a number of mid-size sedans for a

particular year model.

The variability of each year model's average miles per gallon is 1.68. The difference between the

median miles per gallon for each year model's lineup is approximately how many times the

variability?

A. 6

B. 3

C. 4

D. 7

14. The dot plots below show the number of gym members who attended two different aerobics

classes over a six-week period. Each class met three times per week.

The variability for each class is 4. The difference between the mean number of gym members for

each class is approximately how many times the variability?

A. 2

B. 4

C. 3

D. 5

15. A forester measured the diameter of 20 randomly selected pine trees from two different

forests in inches. He measured the diameter of 10 trees in Pebble Brook forest and 10 trees in

Piney Woods forest. He then calculated the following statistical information.

Pebble Brook

Piney Woods





A. The third quartile of diameters is greater for the trees in Pebble Brook than in Piney

Woods.

B. The interquartile range of diameters is greater for the trees in Piney Woods than in

Pebble Brook.

C. The first quartile of diameters is less for the trees in Pebble Brook than in Piney Woods.

D. The median of diameters is greater for the trees in Piney Woods than in Pebble Brook.

16. The dot plots below show the number of students present in Mr. King's first and second

period classes each day in April.

The mean absolute deviation for each class period is 1.4. The difference between the mode

number of students present for each class period is how many times the mean absolute deviation?

A. 6

B. 5

C. 4

D. 7

17. The dot plots below show the number of hummingbirds spotted per day at two different

feeders.

The variability at each feeder is 3.168. The difference between the median number of

hummingbirds spotted per day at each feeder is approximately how many times the variability?

A. 5

B. 2

C. 4

D. 3

18. A certain college randomly selected 30 freshman students who completed college algebra

during their first semester. Fifteen students were chosen from students who took the course at

night and 15 students were chosen from students who took the course during the day. The

following statistical information was calculated from their final grades.

Day

Night

Mean 76 68

Median 68 72

Mode 64 72

Range 38 53

Based on these samples, what generalization can be made? (Assume that a score of 70 or greater is a passing score.)

A. The mean score for the day students was higher than the mean score for the night

students.

B. The median score for the day students was higher than the median score for the night

students.

C. The mean score for the night students was higher than the mean score for the day

students.

D. The range of scores was larger for the day students than for the night students.

19. A survey was conducted on the salaries of 20 randomly selected college graduates with

degrees in the same subject area. Each person surveyed graduated within the same 5-year period.

Ten of the people surveyed attended a private university, while the other 10 people surveyed

attended a public university of roughly the same size.

Private

Public

First Quartile $58,000 $35,000

Second Quartile (Median) $71,000 $42,000

Third Quartile $85,000 $54,000


A. The top twenty-five percent of both the private and public university graduates surveyed

earned more than $50,000 annually.

B. The interquartile range for private universities is $27,000 more than for public

universities.

C. The top ten percent of both the private and public university graduates surveyed earned

more than $60,000 annually.

D. The interquartile range for public universities is $19,000 more than for private

universities.

20. A survey was conducted on ice cream sales. An ice cream shop was randomly selected, and

the sales amounts from 12 summer days and 12 spring days were analyzed. The statistics from

the sales of the ice cream shop are shown below.

Spring

Summer





A. At least $2,400 of ice cream was sold for over half the days in spring and summer.

B. The largest amount of money was made on a summer day.

C. More than $2,300 of ice cream was sold for at least half the days in spring and summer.


21. A survey was conducted on the salaries of 30 randomly selected households in two different

cities. Fifteen of the people surveyed resided in Cartisia, while the other 15 resided in

Pascalville.

Cartisia

Pascalville





A. At least half of the household incomes in both towns are $50,000 or greater.

B. Not enough information is provided to draw any of these conclusions.

C. At least half of the household incomes in both towns are $50,000 or less.

D. The median in Cartisia is $18,000 more than in Pascalville.

22. The age at retirement of 30 randomly selected men from two different towns was collected.

Fifteen of the men were from Newtonia and 15 of the men were from Euclidia. The following

statistical information was calculated from the data.

Newtonia

Euclidia

Mean 65 73

Median 60 72

Mode 62 62

Range 50 33


A. The range of retirement ages is greater in Euclidia than in Newtonia.

B. At least half of the men in both towns will retire before they reach 60 years of age.

C. More men retire in Euclidia than in Newtonia.

D. The most common age for retirement in Newtonia is the same as the most common age

for retirement in Euclidia.

23. A survey was conducted on the salaries of 20 randomly selected college graduates with

degrees in the same subject area. Each person surveyed graduated within the same 5-year period.

Ten of the people surveyed attended a private university, while the other 10 people surveyed

attended a public university of roughly the same size.

Private

Public





A. The top ten percent of both the private and public university graduates surveyed earned

more than $60,000 annually.

B. The interquartile range for public universities is $19,000 more than for private

universities.

C. The interquartile range for private universities is $27,000 more than for public

universities.

D. The top twenty-five percent of both the private and public university graduates surveyed

earned more than $50,000 annually.

24. The dot plots below show the number of flags sold each day at two stores last month.

The variability at each store is 2.4. The difference between the mean number of flags sold at each

store is approximately how many times the variability?

A. 3

B. 5

C. 4

D. 2

25. At a middle school campus, the number of text messages sent by males and females were

analyzed. Twelve random female students and 12 random male students were asked how many

text messages they sent that day. The following data was calculated from the number of text

messages sent during the day for males and females.

Females

Males

Mean 112 99

Median 68 52

Mode 78 78

Range 84 76


A. A female sent the most number of text messages out of both groups.

B. The modes of text messages sent by both males and females are the same.


D. Males sent more total text messages than females.

26. The age at retirement of 30 randomly selected men from two different towns was collected.

Fifteen of the men were from Newtonia and 15 of the men were from Euclidia. The following

statistical information was calculated from the data.

Newtonia

Euclidia

Mean 65 73

Median 60 72

Mode 62 62

Range 50 33


A. The most common age for retirement in Newtonia is the same as the most common age

for retirement in Euclidia.

B. More men retire in Euclidia than in Newtonia.

C. The range of retirement ages is greater in Euclidia than in Newtonia.

D. At least half of the men in both towns will retire before they reach 60 years of age.

27. The dot plots below show the number of blooms on miniature rose bush plants at two garden

supply stores.

The mean absolute deviation for each store is 1.5. The difference between the median number of

blooms per plant for each store is how many times the mean absolute deviation?

A. 7

B. 9

C. 8

D. 6

28. The morning and afternoon art classes made fans using peacock feathers. The dot plots below

show the number of feathers used by students in the two classes.

The mean absolute deviation for each class is 1.5. The difference between the mode number of

feathers used by students for each class is how many times the mean absolute deviation?

A. 4

B. 3

C. 7

D. 6

29. A wildlife biologist captured and released 26 male whitetail deer from two different forests

and weighed them to the nearest pound. She captured 13 deer from Big Rock forest and 13 deer

from Red River forest. She then calculated the following statistical information.

Big Rock

Red River

First Quartile 151.5 143

Second Quartile (Median) 160 155



A. The median is higher for Red River forest than for Big Rock forest.

B. Red River forest has more deer that weigh 160 pounds or more compared to Big Rock

forest.

C. Big Rock forest has more deer that weigh 155 pounds or less compared to Red River

forest.

D. The interquartile range for Red River forest is greater than the interquartile range for Big

Rock forest.

30. The dot plots below show the number of minutes it took Ellen to drive to work on workdays

in May and June.

The mean absolute deviation for each month is 1.6. The difference between the mode number of

minutes driven to work for each month is approximately how many times the mean absolute

deviation?

A. 4

B. 2

C. 5

D. 3

31. At a car dealership, the sales records of weekdays and weekends were examined. Ten of the

days examined were weekdays and 10 of them were weekend days. The following statistical

information was calculated from the number of sales made during weekdays and weekends.

Weekday

Sales

Weekend

Sales

Mean 15 18

Median 13 19

Mode 14 21

Range 10 13


A. Less cars were sold on the weekdays than on the weekends.

B. More cars were sold on the weekdays than on the weekends.


D. The same number of cars were sold on the weekends as on the weekdays.

32. A basketball team plays half of its games during the day and half at night. Ten scores from

day games and ten scores from night games were randomly selected by the team's statistician.

The following statistical information was calculated from the final game scores.

Day

Night

Mean 58 72

Median 46 63

Mode 50 70

Range 21 33


A. The basketball team scored the same number of points in day games as night games.

B. The basketball team scored more points in day games than in night games.

C. The basketball team scored more points in night games than in day games.


33. A survey was conducted on ice cream sales. An ice cream shop was randomly selected, and

the sales amounts from 12 summer days and 12 spring days were analyzed. The statistics from

the sales of the ice cream shop are shown below.

Spring

Summer





A. At least $2,400 of ice cream was sold for over half the days in spring and summer.

B. Not enough information is provided to draw any of these conclusions.

C. The largest amount of money was made on a summer day.

D. More than $2,300 of ice cream was sold for at least half the days in spring and summer.

34. The dot plots below show the number of hours that part-time employees worked at two stores

last week.

The variability at each store is 1.85. The difference between the mode number of hours worked

per employee at each store is approximately how many times the variability?

A. 4

B. 5

C. 3

D. 6

35. The dot plots below show the number of pages Mandee read per day for two books in a

series.

The mean absolute deviation for each book is 1.25. The difference between the median number

of pages read per day for each book is how many times the mean absolute deviation?

A. 4

B. 3

C. 5

D. 2

36. A fitness expert was doing research on football teams. He randomly selected 10 players from

a college team and 10 players from a professional team. The players were weighed and the

statistics are shown below.

College

Professional


Second Quartile (Median) 232 235



A. The median weight of the college players is greater than the median weight of the

professional players.

B. Out of the college and professional players, the professional players have the heaviest

player.


D. The median weight of the professional players is greater than the median weight of the

college players.

19. central tendency and variability

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