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: Numbers of letters: 1-4 4-7 7-10 10-13 13-16 16-19 Number surnames: 6 30 40 16 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.

Question

Philoid · Accepted Answer

Class interval	Mid value (x)	Frequency (f)	fx	Cumulative frequency
1-4	2.5	6	15	6
4-7	5.5	30	165	36
7-10	8.5	40	340	76
10-13	11.5	16	185	92
13-16	14.5	4	58	96
16-19	17.5	4	70	100
Total		N=100

Mean= =

We have, N= 100,

N/2 = 50

Hence, median class =7-10, such that

l=7, f’=40, f=36, h=3

Median = l +

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

=

Numbers of letters:	1-4	4-7	7-10	10-13	13-16	16-19
Number surnames:	6	30	40	16	4	4