Question

100 surnames were randomly picked up from a local telephone directly 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.

Answer 1

Mean = \(\frac{\sum fx}{N}=\frac{832}{100}=8.32\)

We have, 

N= 100, 

N/2 = 50 

Hence, 

median class =7-10, such that 

l=7, f’=40, f=36, h=3

Median \(=I+\frac{\frac{n}{2}-f}{f^{1}}\times h\)

\(=7+\frac{50-36}{40}\times3=8.05\)

Here, 

we may observe that maximum class frequency is 40 belonging to the class interval 7-10 

So, 

modal class= 7-10 

Lower limit, l= 7 

f₀=30, f₂=16, f=40,h = 3

Mode = \(I = (\frac{f-f_0}{2f-f_0-f_2})h\)

\(=7+(\frac{40-30}{2(40)-30-16})3\)

\(=7+\frac{30}{34}=7.88\)