Lesson 2: Comparing Data Sets

Property

Use measures of center and measures of variability to compare two data sets.
To determine if there is a meaningful difference between groups, express the difference between their centers as a multiple of their measure of variability.
When the difference between means is large compared to the variability, the data sets show a significant difference.

Examples

Property

Outliers are values that are significantly different from the rest of the data in a set.
An outlier appears separated from the main cluster of data points and can often be identified visually in data displays like dot plots, histograms, or box plots.
Outliers should always be examined in context to determine if they represent errors, unusual but valid observations, or the most important data points in the set.

Examples

Property

The mean absolute deviation (MAD) is a measure of variability (or spread) of the data that uses each data value.
To compute the MAD, first find the mean of the data set, $\overline{x}$.
Then, find the absolute deviation of each data point from the mean: $|x - \overline{x}|$.
The mean absolute deviation is the mean of these absolute deviations for all the data points.

Examples

• For the data set {3, 5, 7, 9}, the mean is 6. The absolute deviations are $|3-6|=3$, $|5-6|=1$, $|7-6|=1$, and $|9-6|=3$. The MAD is $\frac{3+1+1+3}{4} = 2$.
• A cat's daily nap times in hours are 14, 15, 16, 15. The mean is 15 hours. The absolute deviations are $|14-15|=1$, $|15-15|=0$, $|16-15|=1$, and $|15-15|=0$. The MAD is $\frac{1+0+1+0}{4} = 0.5$ hours.
• Group A's scores {80, 85, 90} have a MAD of 3.33. Group B's scores {70, 85, 100} have a MAD of 10. Group B's scores have greater variability.

Explanation

The MAD tells you the average distance of each data point from the mean. A larger MAD indicates that the data values are more spread out, while a smaller MAD means the data points are clustered closely around the mean.