Question

In a study about viral fever, the number of people affected in a town were noted as Find its standard deviation

Age in years	0−10	10−20	20−30	30−40	40−50	50−60	60−70
Number of people affected	3	5	16	18	12	7	4

Answer 1

Assumed mean = 35

Age in year	Number of people affected fi	Mid value xi	di = xi − A = xi − 35	fidi	fidi2
0−10	3	5	− 30	− 90	2700
10−20	5	15	− 20	− 100	2000
20−30	16	25	− 10	− 160	1600
30−40	18	35	0	0	0
40−50	12	45	10	120	1200
50−60	7	55	20	140	2800
60−70	4	65	30	120	3600
	`sumf_"i"` = 65			`sumf_"i""d"_"i"` = 30	`sumf_"i""d"_"i"^2` = 13900

Here `sumf_"i"` = 65, `sumf_"i""d"_"i"` = 30, `sumf_"i""d"_"i"^2` = 13900

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

= `sqrt(13900/65 - (30/65)^2`

= `sqrt(213.85 - (0.46)^2`

= `sqrt(213.85 - 0.21)`

= `sqrt(213.64)`

= 14.616

= 14.62

∴ Standard deviation (σ) = 14.62