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Statistics

Question 6:

100 surnames were randomly picked up from a local telephone directory and the frequency distribution of the number of letters in the English alphabets in the surnames was obtained as follows:

Number of letters

1 − 4

4 − 7

7 − 10

10 − 13

13 − 16

16 − 19

Number of surnames

6

30

40

6

4

4

Determine the median number of letters in the surnames. Find the mean number of letters in the surnames? Also, find the modal size of the surnames.

Answer:

The cumulative frequencies with their respective class intervals are as follows.

Number of letters

Frequency (fi)

Cumulative frequency

1 − 4

6

6

4 − 7

30

30 + 6 = 36

7 − 10

40

36 + 40 = 76

10 − 13

16

76 + 16 = 92

13 − 16

4

92 + 4 = 96

16 − 19

4

96 + 4 = 100

Total (n)

100

It can be observed that the cumulative frequency just greater than is 76, belonging to class interval 7 − 10.

Median class = 7 − 10

Lower limit (l) of median class = 7

Cumulative frequency (cf) of class preceding median class = 36

Frequency (f) of median class = 40

Class size (h) = 3

Median

= 8.05

To find the class ...

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