Question

# Calculate the sample mean and sample variance for the following frequency distribution of hourly wages for...

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

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