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:
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.
Solution:
Cumulative frequency greater than
is 76
So, median class = 7-10
Median
where, l = lower limit of median class = 7
n = number of observations = 100
cf = cumulative frequency of class preceding the median class = 36
f = frequency of median class = 40
h = class size (assuming class size to be equal) = 3
Median
letters
Mean =
letters
Maximum frequency = 40
So, modal class = 7-10
Lower limit of the modal class
Size of the class interval
Frequency of the modal class
Frequency of the class proceeding the modal class
Frequency of the class succeeding the modal class
Mode
Mode
letters
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