S - Measures of Variability Lesson

Math_Lesson_TopBanner.png Measures of Variability

The range, mean absolute deviation, and interquartile range are all ways to measure the variability for a set of data.

  • The range measures how spread out the data is. To find the range, subtract the smallest value from the largest value in a set of data.
  • The mean absolute deviation (MAD) is the average distance of each data value from the mean.  
  • A small MAD means the values do not vary much from the mean. A large MAD means that the values vary greatly from the mean.

To find the mean absolute deviation (MAD):

  1. Find the mean.
  2. Find the distance between each data value and the mean. That is, find the absolute value of the difference between each data value and the mean.
  3. Find the average of those differences.

Box and Whisker Plot

Before starting any plots, the data should be arranged in numerical order.

  • First, you need to find the median of the data. This is the middle score. If there is an even number, average the middle two numbers. The median is also the 2nd quartile.
  • Second, divide the data set in half. If the data set is odd, do not include the middle number. Find the median of each the lower set of numbers and the upper set of numbers. The median of the lower set of numbers is the 1st quartile. The median of the upper set of numbers is the 3rd quartile.
  • The last information you need is which are the smallest and largest numbers in the data set.

Follow the examples to see how to use this information to construct a box and whisker plot. You'll also be asked for the range of the data. The range is simply the largest number minus the smallest number in the data set.

Box-and-whisker plots are helpful in interpreting the distribution of data. From looking at a box and whisker plot, you can tell the median and range very quickly.

It is useful to see data displayed graphically. One way to do this is to use the box and whisker plot. A box and whisker plot is a diagram that summarizes data using the median, the upper and lower quartiles, and the extreme values (minimum and maximum). Box and whisker plots are also known as box plots.  

Remember they are constructed using a five-number summary of the data:

  1. Minimum
  2. Q1 (lower quartile)
  3. Q2 (median)
  4. Q3 (upper quartile)
  5. Maximum

The interquartile range (IQR) is the difference between the first and third quartiles.

Interquartile Range = Q3 (upper quartile) - Q1 (lower quartile)

Watch the videos below to learn more about reading and constructing a box plot to read measures of variability. Click the arrow in the upper right corner to move to the next video.

Graphic Representations of Data Assignment

Download the "Graphic Representation of Data Assignment" by clicking here. Be sure to work all of the problems on paper. You will use these problems and solutions to complete the "Statistics Homework Quiz 2." Remember you can always go back and review the lessons and videos for more help. Links to an external site.

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