Question

Find the mean, deviation from the mean for each data point, the square of the deviation...

Find the mean, deviation from the mean for each data point, the square of the deviation for each data point, and the standard deviation of these numbers.

8, 55, 25, 21,14, 21, 26

Homework Answers

Answer #1

Solution:

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

Mean = ∑X/n

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

We are given n = 7

Deviation from mean = (X - mean)

Square of the deviation = (X - mean)^2

The calculation table is given as below:

No.

X

(X - mean)

(X - mean)^2

1

8

-16.28571

265.2243502

2

55

30.71429

943.3676102

3

25

0.71429

0.510210204

4

21

-3.28571

10.7958902

5

14

-10.28571

105.7958302

6

21

-3.28571

10.7958902

7

26

1.71429

2.938790204

Total

170

0

1339.428571

Mean = 170/7 = 24.28571429

Standard deviation = Sqrt(1339.428571/6) = Sqrt(223.2380952) = 14.94115441

Standard deviation = 14.94115441

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