Question

Because of advancements in communication and information​ technologies, workers are increasingly able to work from home. The following grouped frequency distribution gives the number​ (in millions) of employed people who work at home for various age groups in a certain year. Complete parts​ (a) and​ (b).	Age ​(in years)	​Midpoint, x	​Frequency, f
	​15-24	19.5	0.5
	​25-34	29.5	1.4
	​35-44	39.5	2.4
	​45-54	49.5	2.5
	​55-64	59.5	2.0
	Over 65	69.5	1.0

​(a) Find the mean age of employed people who work at home.

The mean is

nothing.

​(Type an integer or decimal rounded to the nearest tenth as​ needed.)

​(b) Find the standard deviation.

The standard deviation is

nothing.

​(Type an integer or decimal rounded to the nearest tenth as​ needed.)

Answer 1

Age	Mid Point (x)	Frequency (f)	fx		(x - Mean)	(x - Mean)^2
15-24	19.5	0.5	9.75		-27.24	742.28
​25-34	29.5	1.4	41.3		-17.24	297.39
​35-44	39.5	2.4	94.8		-7.24	52.49
​45-54	49.5	2.5	123.75		2.76	7.59
​55-64	59.5	2	119		12.76	162.69
Over 65	69.5	1	69.5		22.76	517.79
		9.8	458.1			1,780.24

Mean = Sum(fx) / Sum(f)

Mean = 458.1 / 9.8

Mean Age = 46.7449 years

Variance = (x - Mean)^2 / Sum(f)

Variance = 1,780.24 / 9.8

Variance = 181.66

Standard Deviation = Variance^(1/2)

Standard Deviation = 181.66^(1/2)

Standard Deviation = 13.48