Question

Calculate the sample mean and sample variance for the following frequency distribution of hourly wages for a sample of pharmacy assistants. If necessary, round to one more decimal place than the largest number of decimal places given in the data.

Hourly Wages (in dollars)

Class	Frequency
8.76-10.5	32
10.51-12.25	25
12.26-14	44
14.01-15.75	16
15.76-17.5	16

Answer 1

Here we have frequency distribution of hourly wages for a sample of pharmacy assistants as,

Hourly Wages (in dollars)
Class	Frequency
8.76-10.5	32
10.51-12.25	25
12.26-14	44
14.01-15.75	16
15.76-17.5	16

we have to find sample mean and sample variance

Class	Mid Point m	Frequency f	m*f	m^2 * f
8.76-10.5	9.63	32	308.16	2967.5808
10.51-12.25	11.38	25	284.5	3237.61
12.26-14	13.13	44	577.72	7585.4636
14.01-15.75	14.88	16	238.08	3542.6304
15.76-17.5	16.63	16	266.08	4424.9104
	Total	133	1674.54	21758.195

Sample mean is ,

Hence Sample mean = 12.59

Now we find sample variance

Where  

Thus sample variance is 5.11