In worksheet on finding the mean of classified data we will solve various types of practice questions on measures of central tendency. Here you will get 9 different types of questions on finding the mean of classified data.

**1.** The following table gives marks scored by students in an
examination.

**Marks**

0 - 5

5 - 10

10 - 15

15 - 20

20 - 25

25 - 30

30 - 35

35 - 40

**Number of Students**

3

7

15

24

16

8

5

2

(i) Calculate the mean mark, correct to two decimal places.

(ii) Calculate the mean mark by taking the assumed mean a = 17.5

**2.** The following table gives the wages of workers in a
factory:

**Marks**

45 - 50

50 - 55

55 - 60

60 - 65

65 -70

70 - 75

75 - 80

**Number of Students**

5

8

30

25

14

12

6

Calculate the mean by short-cut method.

**3.** The following table gives the weekly wages of workers in
a factory.

**Weekly wages ****(in Dollar)**

50 - 55

55 - 60

60 - 65

65 - 70

70 - 75

75 - 80

80 - 85

85 - 90

**Number of Workers**

5

20

10

10

9

6

12

8

Calculate

(i) the mean

(ii) the number of workers getting weekly wages below $ 80

(iii) the number of workers getting $ 65 or more but less than $ 85 as weekly wages.

**4.** The weights of 50 apples were recorded as given below.
Calculate the mean weight, to the nearest gram, by the step-deviation method.

**Weight (in g)**

80 - 85

85 - 90

90 - 95

95 - 100

100 -105

105 - 110

110 - 115

**Number of Apples**

5

8

10

12

8

4

3

**5.** Find the unknown frequencies in the following
distribution if its mean is known to be 10.8.

**Class Interval**

0 - 4

4 - 8

8 - 12

12 - 16

16 - 20

**Total**

**Frequency**

3

...

...

8

2

20

**6.** Weights of 50 eggs were recorded as below.

**Weight (in g)**

80 - 84

85 - 89

90 - 94

95 - 99

100 -104

105 - 109

110 - 114

**Number of Eggs**

5

10

12

12

8

2

1

(i) Calculate the mean weight of eggs to the nearest gram.

(ii) Calculate the mean weight of eggs by the step-deviation method.

**7.** Taking the assumed mean a = 18, find the mean of the
following distribution.

**Class Interval**

1 - 5

6 - 10

11 - 15

16 - 20

21 - 25

26 - 30

31 - 35

**Frequency**

4

12

7

10

5

6

2

**8.** Find the mean age from the following distribution.

**Age (in Years)**

Under 10

Under 20

Under 30

Under 40

Under 50

Under 60

**Number of Males**

6

10

25

32

43

50

**9.** The number of days 30 workers of a factory were absent in
s year was found to be as below.

2, 14, 50, 72, 9, 48, 61, 60, 75, 39, 4, 8, 26, 62, 70, 58, 29, 77, 64, 43, 56, 67, 45, 58, 69, 76, 6, 50, 17, 66

Prepare the frequency table with overlapping intervals of size 10, and calculate the mean of the number of days the workers were absent.

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

**Answers**

**1.** (i) 18.56

(ii) 18.56

**2.** 62.25

**3.** (i) $ 69

(ii) 60

(iii) 37

**4.** 95.9 g

**5.** 2 and 5 respectively.

**6.** (i) 94 g

(ii) 94 g

**7.** 15.83

**8.** 31.8 years

**9. **

46 days

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