Exercises on Measures of Central Tendency

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There are seven multiple-choice questions in this exercise. Click the letter to select the corresponding answer.

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1. This is the frequency distribution of the ages of students in a class.

Age Frequency

11 7

12 19

13 10

14 4

Find out their mean age.

A

B

C

12

12.3

12.5

D 19

Bingo ！

Mean age

40

41410131912711

3.12

Next question

Age Frequency

11 7

12 19

13 10

14 4

12 is the mode, not the mean. Try again！

Hints:

Return

Age Frequency

11 7

12 19

13 10

14 4

Mean age40

4141013912711

Sorry! You forgot to count the frequencies! Try again!Hints:

Return

Age Frequency

11 712 1913 1014 4

Mean4

114113112111

5.12

Age Frequency

11 112 113 114 1

Mean age = ?

19 is the frequency of 12 year-old. That means there are 19 students who are 12 years old. You should be looking for the mean of the students’ age. Try again!

Hints:

Return

Age Frequency

11 7

12 19

13 10

14 4

Mean age40

4141013912711

2. This is the frequency distribution of the weights of 50 members of a children’s choir.

Weight（ kg） Class mark, x kg Frequency

36-40 38 241-45 43 846-50 48 1151-55 53 1256-60 58 1361-65 63 4

A

B

C

51.8 kg

56-60 kg

50.5 kg

Find out their mean weight.

Bingo ！

Mean weight

Next question

50

463135812531148843238

8.51 (kg)

56-60 kg is the modal class, not the mean weight. Try again! Hints：

Mean weight

Return

Weight（ kg） Class mark, x kg Frequency

36-40 38 241-45 43 846-50 48 1151-55 53 1256-60 58 1361-65 63 4

50

463135812531148843238

Sorry! You forgot to count the frequencies. Try again! Hints：

Return

Mean weightWeight Frequency

1x2x3x

4x

1f

2f

3f

4f4321

44332211

ffff

fxfxfxfx

Weight（ kg） Class mark, x kg Frequency

36-40 38 241-45 43 846-50 48 1151-55 53 1256-60 58 1361-65 63 4

Mean weight= ?

3. The table shows the number of mobile phones owned by 100 families.

Number of mobile phones Frequency

2 23 64 385 166 207 18

Find the mode.

A

B

C

4

4.5

5

D 38

Mode = 4

Bingo ！Mode is the most frequent datum/data in a set of data. Therefore:

Next question

5 is the mean of mobile phones owned by each family, not the mode.

Hints：

Mode is the most frequent datum/data in a set of data.

Return

Try again!

Hints： Mode is the most frequent datum/data in a set of data.

Return

38 is the frequency of 4. That means there are 38 families that have 4 mobile phones. You should be looking for the mode！

Try again!

Sorry, your answer is wrong. Try again!

Hints： Mode is the most frequent data in a set of data.

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4. This is the frequency distribution of the time spent by Kelly on waiting for the bus last week.

Time (minutes) Class mark (minutes) Frequency (days)

1-5 3 06-10 8 1511-15 13 1216-20 18 1221-25 23 1

Find the modal class.A

C

D

12.9 minutes

11-15 and 16-20 minutes

6-10 minutes

B 8 minutes

Bingo ！Modal class is the most frequent class in a set of data. Therefore:

Modal class = 6-10 minutes

Next question

12.9 is the mean of the time spent on waiting for the bus, not the modal class.

Hints： Modal class is the most frequent class in a set of data.

Return

Try again!

8 is the class mark of the class “6-10 minutes”. You should be looking for the modal class of the time spent by Kelly on waiting for the bus in the past 40 days.

Hints： Modal class is the most frequent class in a set of data.

Return

Try again!

Sorry, your answer is wrong. Try again! Hints： Modal class is the most frequent class in a set of data.

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5. This is the frequency distribution of the time spent by 80 students in finishing a 3,000-meter track.

Time（minutes） Class mark (minutes） Frequency (No. of person)

10-15 13 4

16-20 18 9

21-25 23 14

26-30 28 14

31-35 33 9

Find the modal class.A

B

C

16-20 and 31-35 minutes

21-25 and 26-30 minutes

15.3 minutes

Bingo ！Modal class is the most frequent class in a set of data. Therefore:

Modal class = 21-25 and 26-30 minutes

Next question

15.3 minutes is the mean of the time needed to finish a 3,000-meter track, not the modal class!

Hints： Modal class is the most frequent class in a set of data.

Return

Try again!

Sorry, your answer is wrong. Try again!

Hints： Modal class is the most frequent class in a set of data.

Return

2500023000210001900017000150001300011000900070005000

10

20

30

40

50

60

70

80

90

100

0

Salary (dollars)

Cum

ulative frequency (person)

6. This is the cumulative frequency polygon of the salaries of a company’s employees. Find the median.

A

B

C

15000 dollars

15400 dollars

15800 dollars

Bingo ！Since there are 90 employees in the company, there median can be found at the 45th employee. Therefore:

Median=15000 dollars

Next question

Sorry, you didn’t pay attention to the cumulative number of employee.

Since there are 90 employees in the company, there median can be found at the 45th employee. Try again!

Hints：

Return

7. This is the cumulative frequency polygon of rainfall in Island West during the past 40 days. Find the median.

B

C

D

70 mm

77 mm

85 mm

Cu

mu

lative freq

uen

cy (day)

020 40 60 80 100 120

5

10

15

20

25

30

35

40

45

Rainfall amount (mm)

A 20 mm

Bingo ！The median of rainfall in 40 days can be found at the 20th day. Therefore:

Median = 70 mm

End

Sorry, you didn’t pay attention to the cumulative number of days. Try again!

Hints： The median of rainfall in 40 days can be found at the 20th day.

Return

The End