Statistics

Statistics

The standard deviation of the population is only used if we know every single value of the population. Often times, the population is too big and in statistics a sample of the population is often times measured. To calculate the standard deviation of the sample , we have n data values (n = number of observations). Therefore, variance is calculated differently. Instead of dividing by the number of observations, as we did for the population, we divide by n-1.

All other calculations stay the same!

Take the following example:

If we are given the following values of weights for a sample: 100, 110, 120, 125, 130

We would calculate the variance by the following:

1. Step 1: Find the sample mean. = 117 2. Step 2: Subtract the mean from each value and place the result in column B of the table. 3. Step 3: Square each result and place the squares in column C of the table. = 100+110+120+125+130 5

A

B

C

( − ) 2

−

(−17) 2 = 289

100 100 − 117 = −17

(−7) 2 = 49

110 120 125

110 − 117 = −7 120 − 117 = 3 1 25 − 117 = 8

3 2 = 9 8 2 = 64

13 2 = 169

130 1 30 − 117 = 1 3

∑( − ) 2

D

289 + 49 + 9 + 64 + 169 = 580

4. Step 4: Find the sum of the squares in Column C (see column D). 5. Step 5: Divide the sum by − 1 to get the variance.

∑( − ) 2 − 1

580 5 − 1

= 2 =

=

= 145

6. Step 6: Take the square root to get the standard deviation.

= √ 2 = √145 ≈ 12.04

© 2015

Achieve

Page 51 of 94