Question

The following data, which was provided from a sample of 158 Mass Mutual employees, shows how many phone calls they receive while they are at work.

Phone calls (per day):              Frequency:

8-11                                         18

12-15                                       23

16-19                                       38

20-23                                       47

24-27                                       32

What is the standard deviation of the grouped data?

	a.	4.5 calls
	b.	5.237 calls
	c.	4.998 calls
	d.	5.077 calls

Answer 1

Solution:

Given that,

Class	Frequancy	Mid Value	d = x - A /h	f*d	f*d2
8 - 11	18	9.5	-2	-36	72
12 - 15	23	13.5	-1	-23	23
16 - 19	38	17.5	0	0	0
20 - 23	47	21.5	1	47	47
24 - 27	32	25.5	2	64	128
	n = 158			fd = 52	fd2 = 270

Sample standard deviation is S

S =  ( fd² - (( fd )² / n) n -1 ) *h

= ( 270 ) - (( 52 )² / 158 ) 157*4

= (270 - 17.1139) /157*4

= 252.8861/ 157*4

= 6.107*4

= 1.2691*4

= 5.0766

Sample standard deviation is S = 5.077

Answer d. is correct.