Question

For the following data, approximate the mean and sample standard deviation of the number of emails received per day. (Round to 2 decimal places.)

Emails(per day)	Frequency
8-11	3
12-15	34
16-19	25
20-23	8
24-27	27

Answer 1

Solution :-

Given that,

Class (1)	Frequency (f) (2)	Mid value (x) (3)	d=x-Ah=x-17.54 A=17.5,h=4 (4)	f⋅d (5)=(2)×(4)	f⋅d2 (6)=(5)×(4)
8 - 11	3	9.5	-2	-6	12
12 - 15	34	13.5	-1	-34	34
16 - 19	25	17.5=A	0	0	0
20 - 23	8	21.5	1	8	8
24 - 27	27	25.5	2	54	108
---	---
	n=97			∑f⋅d=22	∑f⋅d2=162

Mean ˉx=A+∑fd/n⋅h

=17.5+22/97⋅4

=17.5+0.2268⋅4

=17.5+0.9072

=18.41

Sample Standard deviation S=( f.d^2(f.d2)/n/n-1.h

=√162-(22)²/97/96⋅4

=√162-4.9897/96⋅4

=√157.0103/96⋅4

=√1.6355⋅4

=1.2789⋅4

=5.12