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	5.4%	9.8%	19.8%	29.2%	25.5%	8.7%	1.6%

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.

(e) 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	0.054	1.323	32.4135
34.5	0.098	3.381	116.6445
44.5	0.198	8.811	392.0895
54.5	0.292	15.914	867.313
64.5	0.255	16.4475	1060.864
74.5	0.087	6.4815	482.8718
84.5	0.016	1.352	114.244
Sum	1	53.71	3066.44

Mean = = X * P(X) = 53.71

Standard deviation =

=X ² * P(X) - ²

=  3066.44 - 53.71²

= 13.48