Question

Age range (yr)	20-29	30-39	40-49	50-59	60-69	70-79	80+
Midpoint x	24.5	34.5	44.5	54.5	64.5	74.5	84.5
Percent of nurses	5.6%	9.1%	19.3%	29.7%	24.5%	10.1%	1.7%

What was the age distribution of nurses in Great Britain at the time of Florence Nightingale? Suppose we have the following information.  Note: In 1851 there were 25,466 nurses in Great Britain.

Compute the standard deviation σ for ages of nurses shown in the distribution. (Round your answer to two decimal places.)

Answer 1

Solution :

x	P(x)	x * P(x)	x2 * P(x)
24.5	0.056	1.372	33.614
34.5	0.091	3.1395	108.3128
44.5	0.193	8.5885	382.1883
54.5	0.297	16.1865	882.1643
64.5	0.245	15.8025	1019.261
74.5	0.101	7.5245	560.5753
84.5	0.017	1.4365	121.3843
Sum	1	54.05	3107.5

Mean = = X * P(X) = 54.05

Standard deviation =

=X ² * P(X) - ²

=  (3107.5 - 54.05²)

= 13.64