Some surnames were picked up from a local telephone directory and the frequency distribution of the number of letters of - Maths - Statistics

Question

Some surnames were picked up from a local telephone directory and
the frequency distribution of the number of letters of the English
alphabets was obtained as follows:

Number of letters
1-4
4-7
7-10
10-13
13-16
16-19

Number of surnames
10
25
35
x
12
8

If it is given that mode of the distribution is 8, then find the
missing frequency (x)

Manbar Singh · Accepted Answer

We have,mode = 8So, modal class = 7-10Lower limit of modal class, l = 7Frequency of modal class, f1 = 35Frequency of the class preceding modal class = f0 = 25Frequency of class succeeding modal class = f2 = xclass size, h = 3Now, mode = l + f1 - f02f1 - f0 - f2×h⇒8 = 7 + 35 - 252×35 - 25 - x×3⇒1 = 1070 - 25 - x×3⇒45-x = 30⇒x = 45 - 30⇒x = 15

Number of letters	1-4	4-7	7-10	10-13	13-16	16-19
Number of surnames	10	25	35	x	12	8