Mod 2 Variability Ch 2

Variance

Measure of how spread out a set of scores are; average of the squared deviations fron the mean

Deviation Score

A score subtracted from the mean

Squared Deviation Score

Square of the difference between a score and the mean

Sum of Squared Deviations

Total of each scores squared difference from the mean.

4 Steps to Find Variance

1. Subtract the mean from each score

2. Square each of these deviation scores (multiply each by itself)

3. Add up the squared deviation scores ( Sum of the deviation score should always be 0 or close to!)

4. Divide the sum of squared deviations by the number of scores

SD vs. Variance

• Standard deviation measures how spread out numbers are from the mean.

• Variance calculates the average degree to which each number is different from the mean.

Standard Deviation

Square root of the average of the squared deviations from the mean; the most common descriptive statistic for variation. Approximately the average amount that scores in a distribution vary from the mean

Standard Deviation Steps

1. Figure the variance

2. Take the square root

Ex:) If the Variance is 100 the Standard Deviation is 10.

V = 9 SD = 3

SD²

Variance

SD

Standard Deviation

Variance Formula

$$SD^2 = \frac{\sum (X - M)^2}{N}$$

Sum of Squared Deviations Formula

$$\sum (X - M)^2$$

Deviation Score Formula

$$X - M$$

$X$ (in the variance formula)

Each individual score

$M$ (in the variance formula)

The mean of the distribution

$$\sum$$

Sum sign; indicates to add up all of the following scores

$N$ (in the variance formula)

The total number of scores

SS

The variance formula can be written using SS instead of $\sum (X - M)^2$

Ex:) SD² = SS / N

Sum of Squares (SS)

Sum of squared deviations

Exclusive Range

High score - Low score

Inclusive Range

High score - Low score + 1

Range

Measure of where the beginning and end are in a set

Interquartile Range

Measure of where the bulk of the values lie