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4 Tutorials that teach Measures of Variation
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Measures of Variation
Common Core: 6.SP.3 S.ID.2

Measures of Variation

Description:

This lesson will introduce measures of variation.

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Tutorial

What's Covered

This tutorial is going to explain different measures of variation and why they're necessary. You will learn about:

  1. Spread
  2. Variation

1. Spread

Different data sets will have different measures of variation, and it’s thus important to understand this spread when examining data.

Term to Know

Measures of Variation/Spread

Statistical measures that indicate how close values are to the center of the distribution. For every measure of variation, a large number indicates the data are very spread out, and a small number indicates the values are very close together.

It's not good enough to report just an average, or a measure of center when you're talking about a data set.

Example   Suppose I was going to compare and contrast the January high, low, and average temperatures for Buffalo Grove, Illinois versus Valdez, Alaska.


Low

High

Average

Buffalo Grove

12°

28°

21°

Valdez

15°

25°

21°

The average for both of these cities is 21 degrees in January. However, if you look at the typical high temperature in Buffalo Grove, it's a little higher than the typical high temperature in Valdez. And the low temperature in Buffalo Grove is a little bit lower than the low temperature in Valdez.

Buffalo Grove's temperatures, although they average the same as Valdez, are a little bit more variable. That means that the data is spread out a little bit more. It gets a little colder at night and a little warmer in the day. Valdez's temperatures seem a little bit more consistent. The data is not as spread.

Big Idea

Because the different data sets have such different spreads, it would be inappropriate to just compare them based on their averages.


2. Variation

It is important to understand how variable the values around the measure of center (whichever you are using) are.

Just like measures of center, there are several measures of spread:

  1. range
  2. standard deviation
  3. interquartile range.

All of these are covered in more detail in other tutorials.

Whatever measure of variation you use, high and low values are indicative of different things:

  • A high value means that the data set is not consistent, that it's more spread out.
  • A low value indicates that the values are not very spread out, that they're tightly clustered together. When the data does deviate from the center, it's not by very much.

You can have measures of spread or measures of variation that are zero, which would indicate that all the data values are, in fact, the same.


Summary

Variation indicates the extent to which the data set values are close together. There are many ways to measure variation and all of those methods have a simple rule: a high value means that the data are more varied and a smaller value means that the data are less varied. Variation and spread are synonyms that will be used fairly extensively throughout these tutorials.

Thank you and good luck!

Source: THIS WORK IS ADAPTED FROM SOPHIA AUTHOR JONATHAN OSTERS

TERMS TO KNOW
  • Measures of Variation/Spread

    Statistical measures that indicate how close values are to the center of the distribution. For every measure of variation, a large number indicates the data are very spread out, and a small number indicates the values are very close together.