**Descriptive statistics** describe a set of data. These include **measures of central tendency, measures of variability, and frequencies.**

#### Measures of Central Tendency

These measures attempt to explain a set of data with a variety of ways. The three most common measures of central tendency are:

**Mean (M or x̄):**is the average of a set of data. It is the sum of all the data points divided by the number of data points.**Median:**is the middle number if the data is sorted in the numerical order.**Mode:**is the most occurring score in the data set.

**Example:** If the data set included: 2, 3, 3, 4, 5, 6, 6, 6, 7, 8; the mean would be (2+3+3+4+5+6+6+6+7+8)/10 = 5; the median would be (5+6)/2 (since there is no single middle number): 5.5; and the mode would be 6.

For **Nominal variables**, you can only use Mode.

For **Ordinal variables**, you can use Median or Mode.

For** Interval and ratio variables**, you can use all three.

For a bell shaped curve, mean=median=mode. For skewed data, the mean is closer to the skewness with median in the middle.

#### Frequency Graphs

The above graphs are an example of frequency graphs. They are used to organize a set of data. They can assume three type of shapes:

#### Measures of Variability

These measures indicate how much variability (heterogeneity) exists within a set of scores.

**Range:**taken by subtracted the lowest score from the highest one**Variance:**indicates the degree to which scores are scattered around the mean; the average amount of variability in the distribution of scores**Standard Deviation:**how much the scores vary from the mean; the square root of variance.- 68% of the scores fall within the first standard deviation
- 95% of the scores fall within the second standard deviation
- 99% of the scores fall within the third standard deviation