Interquartile Range

Conceptual Explanation

Interquartile Range

Interquartile Range

The interquartile range represents the distance between the 25th percentile and 75th percentile.

Interquartile Range

Interquartile Range

The interquartile range represents the distance between the 25th percentile and 75th percentile.

1 2 3 4 5 6 7 8 9

1

2

3

4

5

Interquartile Range

Interquartile Range

The interquartile range represents the distance between the 25th percentile and 75th percentile.

1 2 3 4 5 6 7 8 9

1

2

3

4

5

25th

percentile

Interquartile Range

Interquartile Range

The interquartile range represents the distance between the 25th percentile and 75th percentile.

50th

percentile

1 2 3 4 5 6 7 8 9

1

2

3

4

5

25th

percentile

Interquartile Range

Interquartile Range

The interquartile range represents the distance between the 25th percentile and 75th percentile.

50th

percentile

1 2 3 4 5 6 7 8 9

1

2

3

4

5

25th

percentile

This is called the MEDIAN

Interquartile Range

Interquartile Range

The interquartile range represents the distance between the 25th percentile and 75th percentile.

50th

percentile

1 2 3 4 5 6 7 8 9

1

2

3

4

5

25th

percentile75th

percentile

Interquartile Range

Interquartile Range

The interquartile range represents the distance between the 25th percentile and 75th percentile.

50th

percentile

1 2 3 4 5 6 7 8 9

1

2

3

4

5

25th

percentile75th

percentile

This means that 25% of the scores fall below this point.

Interquartile Range

Interquartile Range

The interquartile range represents the distance between the 25th percentile and 75th percentile.

50th

percentile

1 2 3 4 5 6 7 8 9

1

2

3

4

5

25th

percentile75th

percentile

This means that 25% of the scores fall below this point.

This means that 75% of the scores fall below this point.

Interquartile Range

Interquartile Range

The interquartile range represents the distance between the 25th percentile and 75th percentile.

1 2 3 4 5 6 7 8 9

1

2

3

4

5

25th

percentile75th

percentile

Interquartile Range

Interquartile Range

The interquartile range represents the distance between the 25th percentile and 75th percentile.

1 2 3 4 5 6 7 8 9

1

2

3

4

5

25th

percentile75th

percentile

Interquartile Range

Interquartile Range

The interquartile range represents the distance between the 25th percentile and 75th percentile.

1 2 3 4 5 6 7 8 9

1

2

3

4

5

25th

percentile75th

percentile

50% of the scores fall between these two

points

Interquartile Range

Interquartile Range

The interquartile range represents the distance between the 25th percentile and 75th percentile.

1 2 3 4 5 6 7 8 9

1

2

3

4

5

25th

percentile75th

percentile

50% of the scores fall between these two

points

This is the Interquartile Range!

Interquartile Range

Purposes of the Interquartile Range (IQR)

Interquartile Range

Purposes of the Interquartile Range (IQR)

The Interquartile Range (IQR) is a helpful measure of spread for two scenarios.

Interquartile Range

Purposes of the Interquartile Range (IQR)

The Interquartile Range (IQR) is a helpful measure of spread for two scenarios.

1. Rank ordered Data

Interquartile Range

Purposes of the Interquartile Range (IQR)

The Interquartile Range (IQR) is a helpful measure of spread for two scenarios.

1. Rank ordered Data

9t 8t 7t

7t

5t

6t

6t

5t 4t

6t

5t

5t

3d 2d 1st

1 2 3 4 5 6 7 8 9

1

2

3

4

5

3d4t

4t

Interquartile Range

Purposes of the Interquartile Range (IQR)

The Interquartile Range (IQR) is a helpful measure of spread for two scenarios.

1. Rank ordered Data

9t 8t 7t

7t

5t

6t

6t

5t 4t

6t

5t

5t

3d 2d 1st

1 2 3 4 5 6 7 8 9

1

2

3

4

5

3d4t

4t First

Interquartile Range

Purposes of the Interquartile Range (IQR)

The Interquartile Range (IQR) is a helpful measure of spread for two scenarios.

1. Rank ordered Data

9t 8t 7t

7t

5t

6t

6t

5t 4t

6t

5t

5t

3d 2d 1st

1 2 3 4 5 6 7 8 9

1

2

3

4

5

3d4t

4t FirstLast

Interquartile Range

Purposes of the Interquartile Range (IQR)

The Interquartile Range (IQR) is a helpful measure of spread for two scenarios.

1. Rank ordered Data

2. Highly Skewed Data

Interquartile Range

Purposes of the Interquartile Range (IQR)

The Interquartile Range (IQR) is a helpful measure of spread for two scenarios.

1. Rank ordered Data

2. Highly Skewed Data

1 2 3

3

5

4

4

5 6

4

5

5 7

7 22 23

1 2 3 4 5 6 7 23

1

2

3

4

5

6

6

22

Interquartile Range

Purposes of the Interquartile Range (IQR)

The Interquartile Range (IQR) is a helpful measure of spread for two scenarios.

1. Rank ordered Data

2. Highly Skewed Data

1 2 3

3

5

4

4

5 6

4

5

5 7

7 22 23

1 2 3 4 5 6 7 23

1

2

3

4

5

6

6

22

Mean = 7Median = 5

Interquartile Range

Purposes of the Interquartile Range (IQR)

The Interquartile Range (IQR) is a helpful measure of spread for two scenarios.

1. Rank ordered Data

2. Highly Skewed Data

1 2 3

3

5

4

4

5 6

4

5

5 7

7 22 23

1 2 3 4 5 6 7 23

1

2

3

4

5

6

6

22

IQR

Interquartile Range

Purposes of the Interquartile Range (IQR)

The Interquartile Range (IQR) is a helpful measure of spread for two scenarios.

1. Rank ordered Data

2. Highly Skewed Data

1 2 3

3

5

4

4

5 6

4

5

5 7

7 22 23

1 2 3 4 5 6 7 23

1

2

3

4

5

6

6

22

IQR Standard Deviation = 5.3

Interquartile Range

Purposes of the Interquartile Range (IQR)

The Interquartile Range (IQR) is a helpful measure of spread for two scenarios.

1. Rank ordered Data

2. Highly Skewed Data

1 2 3

3

5

4

4

5 6

4

5

5 7

7 8 9

1 2 3 4 5 6 7

1

2

3

4

5

6

6

IQR

8 9

Standard Deviation = 2.3

Notice how the Standard Deviation drops from

5.3 to 2.3.

Interquartile Range

Purposes of the Interquartile Range (IQR)

The Interquartile Range (IQR) is a helpful measure of spread for two scenarios.

1. Rank ordered Data

2. Highly Skewed Data

1 2 3

3

5

4

4

5 6

4

5

5 7

7 8 9

1 2 3 4 5 6 7

1

2

3

4

5

6

6

IQR

8 9

Standard Deviation = 2.3

Notice how the Standard Deviation drops from

5.3 to 2.3. However the IQR stays

the same.

Interquartile Range

The EndInterquartile Range