Calculate: Standard Deviation

Regardless of how you obtained variance (by dividing by N or by N-1), you calculate the standard deviation by taking the square root of variance.

Take what you calculated variance to be. Put it in your calculator and push this button:

 

The result is the standard deviation.

NOW YOU CHOOSE:
Day 3: Dispersion
A Bit More About Dispersion
Even More About Dispersion
Range
MAD
Sum of Squares
Variance
Standard Deviation
How To Calculate
Range
MAD
Sum of Squares
Variance
Standard Deviation
Formulas For Dispersion
Practice Problems
More Practice Problems
Basic Facts About Dispersion
Vocabulary
Quiz 3
Summary

 

Calculate: Variance

The fourth measure of dispersion is variance. Variance is the Sum of Squares divided by N

Variance of a population is always SS divided by N; regardless whether it is a large population or a small population.

Variance of a large sample (where N is equal to or larger than 30) is calculated like a population. Divide SS by N.

If the sample is small (less than 30), adjust for the small sample size by dividing SS by N-1.

 

NOW YOU CHOOSE:
Day 3: Dispersion
A Bit More About Dispersion
Even More About Dispersion
Range
MAD
Sum of Squares
Variance
Standard Deviation
How To Calculate
Range
MAD
Sum of Squares
Variance
Standard Deviation
Formulas For Dispersion
Practice Problems
More Practice Problems
Basic Facts About Dispersion
Vocabulary
Quiz 3
Summary

Calculate: MAD

Calculate: Sum of Squares

Like range, variance and standard deviation, Sum of Squares (SS for short) is a measure of dispersion. The more inconsistent the scores are (less homogeneous) the larger the dispersion. The more homogenous the scores (alike), the smaller the dispersion.

Using the formula above, let’s go through it, step by step Assume this is the distribution at issue:

X
12
6
5
4
5
10
3

First, each number is squared, and put into another column:

X X²
12 144
6 36
5 25
4 16
5 25
10 100
3  9

 

Second, we sum each column. The sum of the first column is 45. This is called the sum of X.

The sum of the second column is the sum of X-squared. Remember, we squred the scores and then added them up. The sum of the squared-X’s is 355.

Third, we square the sum of X (45 times itself = 2025) and divide it by N.

Since N = 7, we divide 2025 by 7 (which equals 289.29).

Fourth, we recall the sum of the X² and subtract 240.67 from it. So 355 minus 289.29 = 65.71. The Sum of Squares is 65.71.

NOW YOU CHOOSE:
Day 3: Dispersion
A Bit More About Dispersion
Even More About Dispersion
Range
MAD
Sum of Squares
Variance
Standard Deviation
How To Calculate
Range
MAD
Sum of Squares
Variance
Standard Deviation
Formulas For Dispersion
Practice Problems
More Practice Problems
Basic Facts About Dispersion
Vocabulary
Quiz 3
Summary