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 (f_{i}) |
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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