Question

The following frequency table summarizes the distances in miles of 100 patients from a regional hospital.
Distance          Frequency     

0-4                   20

4-8                   25

8-12                 30

12-16               20

16-24               5
Calculate the sample variance and standard deviation for this data (since it is a case of grouped data- use group or class midpoints in the formula in place of X values, and first calculate the sample mean).

need step and sloution

Answer 1

Solution:

The formula for sample variance and sample standard deviation for given data is given as below:

Sample variance = ∑f(x - mean)^2 / (∑f – 1)

Sample standard deviation= Sqrt[∑f(x - mean)^2 / (∑f – 1)]

Sample mean = ∑xf/∑f

The calculation table is given as below:

Mid-point x	f	xf	f(x - mean)^2
2	20	40	871.2
6	25	150	169
10	30	300	58.8
14	20	280	583.2
18	5	90	441.8
Total	100	860	2124

Sample mean = 860/100 = 8.6

Sample variance = 2124/(100 – 1) = 2124/99 = 21.45454545

Sample variance = 21.45454545

Sample standard deviation= Sqrt(21.45454545) = 4.631905165

Sample standard deviation= 4.631905165