Measures of Variation

Measures of Variation

by Lauren Cleeton

​Review

​What is the median?

• ​The value in the center of an ordered list of data. If 2 values appear in the center, it is the mean of those 2 values.

​

​What is the range?

• ​The range is the difference between the highest and lowest data value.

​Measures of Variation

​Quartiles

• ​Values that divide the data into 4 equal parts

​First and Third Quartiles

• ​The first quartile is the median of the data values less than the median.

• The third quartile is the median of the data values greater than the median.

​Interquartile Range

• ​The IQR is the difference between the first and third quartiles.

​Outliers

• ​Outliers are extremely high or low values in reference to the data set.

​First and Third Quartiles

​Find the 1st and 3rd (or lower and upper) quartiles. Look at Step 2.

​Cut/Paste into a new tab to watch!

​

https://www.youtube.com/watch?v=X54Mf0KtJ00

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Multiple Choice

Find the Quartile 1 of these numbers:

2, 3, 4, 5, 5, 5, 7,

• 4

• 6

• 3

• 5

Multiple Choice

Find the Quartile 3 of these numbers:

2, 3, 4, 5, 5, 5, 7,

• 4

• 6

• 3

• 5

​Interquartile Range (IQR)

​Once you have the first and third quartiles, you can find the IQR by subtracting them. Look at step 3.

​Copy and Paste to watch!

https://www.youtube.com/watch?v=0TulXwT_3ck&t=26s​

Multiple Choice

What is the interquartile range of the data set below?

3, 5, 6, 6, 7, 8, 9

• 3

• 6

• 2

• 8

Multiple Choice

Find the IQR using the following data.

50, 60, 82, 86, 94, 110

• 60

• 84

• 34

• 50

​Finding Outliers

​To find the "limits" of the outliers, take first quartile and subtract 1.5 x IQR, and then take the third quartile and add 1.5 x IQR. Watch and learn!

​

​https://www.youtube.com/watch?v=UmKPdxlFAsI&t=211s

Multiple Choice

Identify the outlier for the given data?
23, 34, 27, 7, 30, 26, 28, 31, 34

• 7
• 23
• 31
• 34

Multiple Choice

Find the outlier of the data set.

15, 20, 18, 35, 17, 35, 13

• no outlier

• 35

• 13

• 15

​TIME TO REVIEW!

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Multiple Choice

Find the median from the list of numbers:

60, 58, 52, 48, 60, 67

• 58

• 59

• 60

• 118

Multiple Choice

Find the Quartile 1.

5, 5, 9, 12,18, 22, 25,

• 18

• 12

• 9

• 5

Multiple Choice

Find the Quartile 3.

5, 5, 9, 12,18, 22, 25,

• 22

• 18

• 25

• 12

Multiple Choice

Find the median, first quartile, third quartile, and interquartile range of the data.

32, 53, 72, 66, 47, 54, 49, 67, 71

• Median: 54

  First Quartile: 49

  Third Quartile: 67

  IQR: 18

• Median: 54

  First Quartile: 48

  Third Quartile: 69

  IQR: 21

• Median: 54

  First Quartile: 48

  Third Quartile: 69

  IQR: 22

• Median: 54

  First Quartile: 49

  Third Quartile: 69

  IQR: 20

Multiple Select

What are the correct expressions for using the IQR to determine if there is an outlier that is a lot less and a lot greater than the other values. Hint: Choose 2 expressions.

• Q1 - 1.5(IQR)

• Q3 - 1.5(IQR)

• Q1 + 1.5(IQR)

• Q3 + 1.5(IQR)

Multiple Choice

Use the interquartile range to identify any outliers in the following data.

52, 63, 55, 56, 62, 54, 59, 60, 53, 61, 88

• No outliers.

• 88 is an outlier.