Question

A sample of size n = 10 n=10 is drawn from a population. The data is shown below. 35.8 72.8 55.4 66.2 55.6 45 72.8 51.6 72.8 42.1

What is the range of this data set? range = 37

What is the standard deviation of this data set? (Remember, it is a sample.) Please report the answer with appropriate rounding, reporting 2 more decimal places than the original data. Please, please, please do not calculate the value by hand.

stdev =

Answer 1

Range=Maximum-Minimum

Maximum= 72.8

Minimum= 35.8

Range= 72.8-35.8= 37

Standard deviation for the sample data set: $S=sqrt{rac{(x_i-ar{X})^2}{n-1}}$

Mean:

X = 〉 Xi/n = 570·1/10 = 57.01

(X-Mean) (X-Mean)A2 35.8 -21.21 15.79 1.61 9.19 1.41 45-12.01 15.79 -5.41 15.79 42.1-14.91 449.864 249.324 2.592 84.456 1.988 144.240 249.324 29.268 249.324 222.308 72.8 55.4 66.2 55.6 72.8 51.6 72.8 Mean 57.01 Sum 1682.689