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.
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