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
	${\displaystyle \sum f_{\text{i}}}$ = 65			${\displaystyle \sum f_{\text{i}}{\text{d}}_{\text{i}}}$ = 30	${\displaystyle \sum f_{\text{i}}{\text{d}}_{\text{i}}^2}$ = 13900

Here ${\displaystyle \sum f_{\text{i}}}$ = 65, ${\displaystyle \sum f_{\text{i}}{\text{d}}_{\text{i}}}$ = 30, ${\displaystyle \sum f_{\text{i}}{\text{d}}_{\text{i}}^2}$ = 13900

Standard deviation (σ) = ${\displaystyle \sqrt{\frac{\sum f_{\text{i}}{\text{d}}_{\text{i}}^2}{\sum f_{\text{i}}}-{\left(\frac{\sum f_{\text{i}}{d}_{\text{i}}}{\sum f_{\text{i}}}\right)}^2}}$

= ${\displaystyle \sqrt{\frac{13900}{65}-{\left(\frac{30}{65}\right)}^2}}$

= ${\displaystyle \sqrt{213.85-{\left(0.46\right)}^2}}$

= ${\displaystyle \sqrt{213.85-0.21}}$

= ${\displaystyle \sqrt{213.64}}$

= 14.616

= 14.62

∴ Standard deviation (σ) = 14.62