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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.
Asked by Shamss Last Modified
Answer 
Abhay
The cumulative frequencies with their respective class intervals are as follows.
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 marks of the given class intervals, the following relation is used.
Taking 11.5 as assumed mean (a), di, ui, and fiui are calculated according to step deviation method as follows.
From the table, we obtain
∑fiui = −106
∑fi = 100
Mean, 
= 11.5 − 3.18 = 8.32
The data in the given table can be written as
From the table, it can be observed that the maximum class frequency is 40 belonging to class interval 7 − 10.
Modal class = 7 − 10
Lower limit (l) of modal class = 7
Class size (h) = 3
Frequency (f1) of modal class = 40
Frequency (f0) of class preceding the modal class = 30
Frequency (f2) of class succeeding the modal class = 16
Therefore, median number and mean number of letters in surnames is 8.05 and 8.32 respectively while modal size of surnames is 7.88.
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