ID - Measures of Spread (Lesson)
Measures of Spread
There are a few common measures of spread that you need to know! The range is the difference between the greatest data value and the least data value. The interquartile range (IQR) is the difference between the third and first quartile. The IQR gives you the range of the middle 50% of the data.
Measures of Spread Practice
1. Find the range and IQR of the data set: 4, 2, 1, 8, 1, 5, 7, 2, 6
2. Find the range and IQR of the data set: 11, 17, 20, 5, 12, 18, 6, 21, 13, 14
The greater the measure of spread is, the more spread out the data is. Often, measures of spread are indicators of consistency. Two students' test scores are listed below:
Tom: 90, 90, 80, 100, 99, 81, 98, 82
Lisa: 90, 90, 91, 89, 91, 89, 90, 90
3. Find the mean of Tom's test scores.
4. Find the mean of Lisa's test scores.
5. Find the range of Tom's test scores.
6. Find the range of Lisa's test scores.
7. Who's scores are more consistent? How do you know?
TO VIEW THE SOLUTIONS ONCE YOU HAVE PRACTICED, CLICK HERE. Links to an external site.
Mean Absolute Deviation
Another important measure of spread is the mean absolute deviation (MAD). In order to find the mean absolute deviation, you can make a table like the one below:
First, find the mean. Let's use Tom's test scores and his mean of 90. Remember that the mean is also called "x bar"
|
Scores for Tom |
Subtract the mean from each value |
Find the absolute value of the difference |
|
90 |
90 - 90 = 0 |
|0| = 0 |
|
90 |
90 - 90 = 0 |
|0| = 0 |
|
80 |
80 - 90 = -10 |
|-10| = 10 |
|
100 |
100 - 90 = 10 |
|10| = 10 |
|
99 |
99 - 90 =9 |
|9| = 9 |
|
81 |
81 - 90 = -9 |
|-9| = 9 |
|
98 |
98 - 90 = 8 |
|8|= 8 |
|
92 |
82 - 90 = -8 |
|-8| = 8 |
Next, add up all the values from the third column and find the mean of those values:
MAD = (0+0+10+10+9+9+8+8)/8 = 6.75
Watch this video to try another example:
Outliers
An outlier is a value in a data set that is much greater or much less than the other values. A data value is considered an outlier if the value is smaller than 1.5 times the IQR or if the value is greater than 1.5 times the IQR.
Watch this video to practice determining if a value is an outlier:
Mean Absolute Deviation and Outlier Practice
- Find the mean absolute deviation of the data: 4, 2, 1, 8, 1, 5, 7, 2, 6
- Find the mean absolute deviation of the data: 11, 17, 20, 5, 12, 18, 6, 21, 13, 14
Determine if there are any outliers in the data set:
- 13, 15, 21, 16, 14, 15, 17
- 51, 49, 52, 30, 48, 50, 52, 51
TO VIEW THE SOLUTIONS ONCE YOU HAVE PRACTICED, CLICK HERE. Links to an external site.
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