Box and Whisker Plot

Box and Whisker Plot

5 Number Summary for Odd Numbered Data Sets

Finding the Median of Odd Numbered Data Sets

Once the pieces of data (numbers) are arranged in order from least to greatest, then the middle number of the set is the median

[3, 4, 4, 5, 8, 8, 9, 10,11]

The median for this set of data = 8

Odd Numbered Data Sets

The median splits the data set in half.

[3, 4, 4, 5,] 8, [8, 9, 10,11]

From here we can then find the upper and lower quartiles as well as the upper and lower extremes.

Lower Quartile

The lower quartile is the median of the bottom half of the data (to the left of the median).If the part of the set we are considering has an even number pieces of data, you must find the mean of the two middle pieces of data to get the lower quartile.

[3, 4, 4, 5,] 8, [8, 9, 10,11]

4 + 4 = 8 8 divided by 2 = 4

The lower quartile for this set of data = 4

Upper Quartile

The upper quartile is the median of the top half of the data (to the right of the median).

If the part of the set we are considering has an even number pieces of data, you must find the mean of the two middle pieces of data to get the upper quartile.

[3, 4, 4, 5,] 8, [8, 9, 10,11]9 + 10 = 19; 19 divided by 2 = 9.5

The upper quartile for this data set = 9.5

Interquartile Range

To find the interquartile range, subtract the lower quartile from the upper quartile.

[3, 4,] 4 [4, 5,] 8, [8, 9] 9.5 [10,11]

Upper Quartile – Lower Quartile = _____9.5 – 4 = 5.5

The intequartile range for this data = 5.5

Lower Extreme

The lower extreme is the lowest number in the data set.

[3, 4,] 4 [4, 5,] 8, [8, 9] 9.5 [10,11]

The lower extreme for this data set = 3

Upper Extreme

The upper extreme is the highest number in the data set.

[3, 4,] 4 [4, 5,] 8, [8, 9] 9.5 [10,11]

The upper extreme for this data set = 11

Range

The range of the data can be found by subtracting the lower extreme from the upper extreme.

[3, 4,] 4 [4, 5,] 8, [8, 9] 9.5 [10,11]

11 – 3 = 8The range for this data set = 8

5 Number Summary

[3, 4, 4, 5, 8, 8, 9, 10,11]

Median = 8Lower Quartile = 4Upper Quartile = 9.5Lower Extreme = 3Upper Extreme = 11

Any Questions?

Sample Problem (ODD)

Data Set

[10, 10, 14, 15, 17, 20, 20, 21, 22]


Find the median.

[10, 10, 14, 15, 17, 20, 20, 21, 22]


The median is 17.

[10, 10, 14, 15, 17, 20, 20, 21, 22]


Find the lower quartile.

[10, 10, 14, 15, 17, 20, 20, 21, 22]


The lower quartile is 12.

[10, 10, 14, 15,] 17, [20, 20, 21, 22] 10 + 14 = 24

24 divided by 2 = 12


Find the upper quartile.

[10, 10, 14, 15,] 17, [20, 20, 21, 22]


The upper quartile is 20.5

[10, 10, 14, 15,] 17, [20, 20, 21, 22]20 + 21 = 41

41 divided by 2 = 20.5


Find the lower extreme.

[10, 10, 14, 15,] 17, [20, 20, 21, 22]


The lower extreme is 10.

[10, 10, 14, 15,] 17, [20, 20, 21, 22]


Find the upper extreme.

[10, 10, 14, 15,] 17, [20, 20, 21, 22]


The upper extreme is 22.

[10, 10, 14, 15,] 17, [20, 20, 21, 22]


The 5 Number Summary for the sample problem with an even number of pieces of data is:

[10, 10, 14, 15, 17,20, 20, 21, 22]

Median= 17Lower Quartile = 12Upper Quartile = 20.5Lower Extreme = 10Upper Extreme = 22


Find the interquartile range for the set of data.

[10, 10, 14, 15, 17,20, 20, 21, 22]



The interquartile range is 8.5.

20.5 – 12 = 8.5

[10, 10, 14, 15, 17,20, 20, 21, 22]



Find the range of the data set.

[10, 10, 14, 15, 17,20, 20, 21, 22]


The range is 12.

22 – 10 = 12

[10, 10, 14, 15, 17,20, 20, 21, 22]

Box and Whisker Plot

5 Number Summary for Even Numbered Data Sets

Even Numbered Data Sets

If the data set has an even number of pieces of data, we find the mean of the two middle numbers to find the median of the set

2, 4, 5, 6, 7, 8, 9, 11, 19, 207 + 8 = 15


The median is 7.5

If the data set has an even number of pieces of data, we find the mean of the two middle numbers to find the median of the set

2, 4, 5, 6, 7, 8, 9, 11, 19, 207 + 8 = 15


The median is 7.5


The median splits the data set in half.[ 2, 4, 5, 6, 7] 7.5 [8, 9, 11, 19, 20]

From here we can then find the upper and lower quartiles as well as the upper and lower extremes.

Lower Quartile

The lower quartile is the median of the bottom half of the data (to the left of the median).

[ 2, 4, 5, 6, 7] 7.5 [8, 9, 11, 19, 20]

Lower Quartile for this data = 5

Upper Quartile

The upper quartile is the median of the top half of the data (to the right of the median).[ 2, 4, 5, 6, 7] 7.5 [8, 9, 11, 19, 20]

The upper quartile for this data set = 11

Interquartile Range

To find the interquartile range, subtract the lower quartile from the upper quartile.

Upper Quartile – Lower Quartile = _____

[ 2, 4, 5, 6, 7] 7.5 [8, 9, 11, 19, 20]11 – 5 =6

The intequartile range for this data = 6

Lower Extreme

The lower extreme is the lowest number in the data set.[ 2, 4, 5, 6, 7] 7.5 [8, 9, 11, 19, 20]

The lower extreme for this data set = 2

Upper Extreme

The upper extreme is the highest number in the data set.[ 2, 4, 5, 6, 7] 7.5 [8, 9, 11, 19, 20]

The upper extreme for this data set = 20

Range

The range of the data can be found by subtracting the lower extreme from the upper extreme.[ 2, 4, 5, 6, 7] 7.5 [8, 9, 11, 19, 20]

20 – 2 = 18The range for this data set = 18


[ 2, 4, 5, 6, 7] 7.5 [8, 9, 11, 19, 20]

Median = 7.5Lower Quartile = 5Upper Quartile = 11Upper Extreme = 20Lower Extreme = 2

Any Questions?

Sample Problem

Use the following data set to create a 5 number summary1,2,3,4,5,6,7,8,9,10,11,12

Sample Problem

What is the median?

1,2,3,4,5,6,7,8,9,10,11,12

The median is the mean of 6 and 7

The median is 6.5

Sample Problem

Remember, the median splits the data set in half

[1,2,3,4,5,6] 6.5 [7,8,9,10,11,12]

Sample Problem

What are the quartiles?

[1,2,3,4,5,6] 6.5 [7,8,9,10,11,12]

Remember, if there are an even number of pieces of data in your set, the median is the mean of the middle two numbers

Sample Problem

What are the quartiles?

[1,2,3,4,5,6] 6.5 [7,8,9,10,11,12]

Upper Quartile = 3.5Lower Quartile = 8.5

Sample Problem

What is the upper extreme?What is the lower extreme?

[1,2,3,4,5,6] 6.5 [7,8,9,10,11,12]

Upper Extreme = 12Lower Extreme = 1

Sample Problem

What is the 5 number summary?Median = 6.5Lower Quartile = 3.5Upper Quartile = 8.5Upper Extreme = 12Lower Extreme = 1

Any Questions?

Box and Whisker Plot

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