Question

The rainfall recorded in various places of five districts in a week are given below. Find its standard deviation

Rainfall (in mm)	45	50	55	60	65	70
Number of places	5	13	4	9	5	4

Answer 1

Assumed mean = 60

Rainfall (in mm)	Number of places fi	di = xi − A = xi − 60	fidi	fidi2
45	5	− 15	− 75	1125
50	13	− 10	− 130	1300
55	4	− 5	− 20	100
60	9	0	0	0
65	5	5	25	125
70	4	10	40	400
	`sumf_"i"` = 40		`sumf_"i""d"_"i"` = − 160	`sumf_"i""d"_"i"^2` = 3050

Here N = 40 (N = f_i), `sumf_"i""d"_"i"` = − 160, `sumf_"i""d"_"i"^2` = 3050

Standard deviation (σ) = `sqrt((sumf_"i""d"_"i"^2)/"N" - ((sumf_"i""d"_"i")/"N")^2`

= `sqrt(3050/40 - ((- 160)/40)^2`

= `sqrt(76.25 - ( - 4)^2`

= `sqrt(76.25 - 16)`

= `sqrt(60.25)`

= 7.76

∴ Standard deviation (σ) = 7.76