Understanding Variability in Distributions

Questions and Answers

Central tendency

Range

Standard deviation

Variability (correct)

It is not a precise measure

It is affected by outliers (correct)

It is only applicable to small datasets

It is difficult to compute

Range

Standard deviation (correct)

Mean absolute deviation

Variance

It is less affected by outliers Signup and view all the answers

They have the same central tendency but different variability Signup and view all the answers

9 Signup and view all the answers

Because it can be greatly affected by a single outlier Signup and view all the answers

1.69 Signup and view all the answers

To find the variance Signup and view all the answers

Variance Signup and view all the answers

They are always positive Signup and view all the answers

Finding the square root of the variance Signup and view all the answers

It is primarily used in inferential statistics Signup and view all the answers

SD² Signup and view all the answers

Study Notes

Variability of a distribution is the extent to which scores vary around their central tendency.
Distributions with the same central tendency can have different variabilities.

The range is a simple measure of variability, calculated as the difference between the highest and lowest scores.
Example: Range of self-esteem scores in Table 12.1 is 24 - 15 = 9.
The range can be misleading when there are outliers.

The standard deviation is the average distance between scores and the mean.
Example: Standard deviations of the distributions in Figure 12.4 are 1.69 for the top distribution and 4.30 for the bottom one.
Computing the standard deviation involves:
- Finding the difference between each score and the mean.
- Squaring each difference.
- Finding the mean of these squared differences (variance).
- Finding the square root of the variance.

The variance is the mean of the squared differences between scores and the mean (symbolized as SD²).
The variance is always positive.
Although the variance is a measure of variability, it generally plays a larger role in inferential statistics than in descriptive statistics.