Question

A sample of size n=10n=10 is drawn from a population. The data is shown below. 79.8...

A sample of size n=10n=10 is drawn from a population. The data is shown below.

79.8 80.2 115 115 103.7
90.4 115 98 95.2 87.6



What is the range of this data set?

range =

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 =

Math   Statistics-And-Probability   
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Homework Answers

Answer #1

Solution:

The formula for range and standard deviation are given as below:

Range = Maximum – Minimum

Maximum = 115

Minimum = 79.8

Range = 115 – 79.8

Range = 35.2

Standard deviation = Sqrt[∑(X - mean)^2/(n – 1)]

The calculation table is given as below:

No.

X

(X - mean)^2

1

79.8

330.8761

2

80.2

316.4841

3

115

289.3401

4

115

289.3401

5

103.7

32.6041

6

90.4

57.6081

7

115

289.3401

8

98

0.0001

9

95.2

7.7841

10

87.6

107.9521

Total

979.9

1721.329

Standard deviation = Sqrt[1721.329/(10 – 1)]

Standard deviation = Sqrt(191.2587778)

Standard deviation = 13.82963404

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