Calculating Measures of Center and Variability

Student Summary

The mean absolute deviation, or MAD, and the interquartile range, or IQR, are measures of variability. Measures of variability tell you how much the values in a data set tend to differ from one another. A greater measure of variability means that the data are more spread out, while a smaller measure of variability means that the data are more consistent and are closer to the measure of center.

To calculate the MAD of a data set:

  1. Find the mean of the values in the data set.
  2. Find the distance between each data value and the mean (on the number line):

    |data value – mean|

  3. Find the mean of the distances. This value is the MAD.

To calculate the IQR, subtract the value of the first quartile from the value of the third quartile. Recall that the first and third quartile are included in the five-number summary.

Visual / Anchor Chart

Standards

Building On
6.SP.5.c

Summarize quantitative data sets in relation to their context.

Building Toward
HSS-ID.A.1

Represent data with plots on the real number line (dot plots, histograms, and box plots).

HSS-ID.A.2

Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (inter-quartile range, sample standard deviation) of two or more different data sets.