# Worksheet on Finding the Mean of Arrayed Data

In worksheet on finding the mean of arrayed data we will solve various types of practice questions on measures of central tendency. Here you will get 12 different types of questions on finding the mean of arrayed data.

1. Find the mean.

Variate

50

100

150

200

Frequency

6

3

8

3

2. Find the mean.

Age (in Years)

11

12

13

14

15

16

17

Number of Students

3

4

6

10

8

7

5

3. Find the mean of the following cumulative-frequency distributions.

Variate

5

10

15

20

Cumulative Frequency

6

10

14

16

4. Find the mean of the following cumulative-frequency distributions.

Variate

2

4

6

8

10

12

Cumulative Frequency

7

10

15

22

28

35

5. The mean of the variates 2, 4, 6 and 8 is $$\frac{54}{11}$$, and the frequencies of the first three variates are 3, 2 and 4. Find the frequency of the fourth variate.

6. Find the variates 5, 15, 25, 35 and 45 have the frequencies 2, 10, 8, 7 and x. If the mean of the variates be $$\frac{74}{3}$$ then find x.

7. In the following frequency table, a frequency f is obscure. If the mean of the distribution is 20.6 then find the frequency f.

Variate

10

15

20

25

35

Cumulative Frequency

6

10

14

16

5

8. The mean of the following frequency distribution is 22.5. Find the value of x.

Variate

5

15

25

x

45

Cumulative Frequency

2

4

3

1

2

9. The mark obtained by a set of students in an examination are given below.

Marks

5

10

15

20

25

30

Number of Students

6

4

6

12

x

4

Given that the mean mark of the set is 18, calculate the numerical value of x.

10. The contents of 100 matchboxes were checked to determine the number of matches they contained.

Number of matches

35

36

37

38

39

40

41

Number of Boxes

6

10

18

25

21

12

8

(i) Calculate, correct to one decimal place, the mean number of matches per box.

(ii) Determine how many extra matches would have to be added to the total contents of the 100 boxes to bring the mean up to exactly 39 matches.

11.

 Category A B C D E F G Wages per day      (in Dollar) 50 60 70 80 90 100 110 Number of Workers 2 4 8 12 10 6 8

(i) Calculate the mean wage, correct to the nearest dollar.

(ii) If the number of workers in each category is doubled, what would be the new mean wage?

(iii) If the number of workers in each category is increased by 2, what would be the new mean wage?

12. Calculate the mean of the following distribution.

Variate

1

2

3

4

5

6

Cumulative Frequency

4

7

15

21

31

35

13. The marks of 20 students in a test were as follows.

5, 6, 8, 9, 10, 11, 11, 12, 13, 13, 14, 14, 15, 15, 15, 16, 16, 18, 19, 20

Calculate the mean mark.

14. (i) Apply the short-cut method to calculate the mean (to the nearest dollar) of the following distribution.

Monthly Pocket Money (in Dollar)

100

120

140

160

180

200

Number of Students

5

10

8

6

11

10

(ii) Using assumed mean a = 30, calculate the mean of the following distribution.

Variate

10

20

30

40

50

Cumulative Frequency

12

31

50

67

80

15. The number of hours of TV viewing per month by 30 families of an area are given below.

45, 48, 70, 48, 75, 40, 45, 50, 50, 48, 75, 70, 80, 80, 45, 50, 45, 50, 40, 48, 85, 70, 80, 45, 85, 70, 48, 48, 75, 40

(i) Construct a frequency table for the data.

(ii) Find the mean of the hours of TV watched by the direct method.

(iii) Find the mean of the hours of TV watched by the short-cut method.

Answers on Worksheet on Finding the Mean of Arrayed Data are given below to check the exact answers of the questions.

1. 120

2. 14.3 years

3. 10.625

4. 7.31

5. 2

6. 3

7. 25

8. 35

9. 8

10. (i) 38.1

(ii) 87

11. (i) $85 (ii)$ 85

(iii) 83.75

12. 3.77

13. 13

14. (i) \$ 155.20

(ii) 30

15. (i)

(ii) 58.27 hours

(iii) 58.27 hours

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