Question

Find the standard? deviation, s, of sample data summarized in the frequency distribution table below by using the formula?below, where x represents the class? midpoint, f represents the class? frequency, and n represents the total number of sample values.? Also, compare the computed standard deviation to the standard deviation obtained from the original list of data?values,

11.1

sequals=StartRoot StartFraction n left bracket Summation from nothing to nothing left parenthesis f times x squared right parenthesis right bracket minus left bracket Summation from nothing to nothing left parenthesis f times x right parenthesis right bracket squared Over n left parenthesis n minus 1 right parenthesis EndFraction EndRootn?f•x2??(f•x)2n(n?1)

Interval	20-29	30-39	40-49	50-59	60-69	70-79	80-89
Frequency	1	1	6	1	18	36	35

Answer 1

For the given frequency table the standard? deviation, s, of sample data summarized in the frequency distribution table below by using the formula?

where x represents the class? midpoint, f represents the class? frequency, and n represents the total number of sample values.?

So here the calculations are as below,

	Interval	Class midpoint (x)	frequency (f)	x.f	x^2	x^2.f
	20-29	24.5	1	24.5	600.25	600.25
	30-39	34.5	1	34.5	1190.25	1190.25
	40-49	44.5	6	267	1980.25	11881.5
	50-59	54.5	1	54.5	2970.25	2970.25
	60-69	64.5	18	1161	4160.25	74884.5
	70-79	74.5	36	2682	5550.25	199809
	80-89	84.5	35	2957.5	7140.25	249908.8
Total			98	7181		541244.5

Note that,

So putting the values we get,

Note that the computed standard deviation to the standard deviation obtained from the original list of data?values is 11.1 which is close to 12.4574 but not very close. This hapens because the most of the data is clustered around the tail making it right skewed while there are some values of X initially as well.

Hence the answer.............

Thank you............