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 = 8
The range for this data set = 8
5 Number Summary
[3, 4, 4, 5, 8, 8, 9, 10,11]
Median = 8
Lower Quartile = 4
Upper Quartile = 9.5
Lower Extreme = 3
Upper Extreme = 11
Any Questions?
Sample Problem (ODD)
Data Set
[10, 10, 14, 15, 17, 20, 20, 21, 22]
Sample Problem (ODD)
Find the median.
[10, 10, 14, 15, 17, 20, 20, 21, 22]
Sample Problem (ODD)
The median is 17.
[10, 10, 14, 15, 17, 20, 20, 21, 22]
Sample Problem (ODD)
Find the lower quartile.
[10, 10, 14, 15, 17, 20, 20, 21, 22]
Sample Problem (ODD)
The lower quartile is 12.
[10, 10, 14, 15,] 17, [20, 20, 21, 22]
10 + 14 = 24
24 divided by 2 = 12
Sample Problem (ODD)
Find the upper quartile.
[10, 10, 14, 15,] 17, [20, 20, 21, 22]
Sample Problem (ODD)
The upper quartile is 20.5
[10, 10, 14, 15,] 17, [20, 20, 21, 22]
20 + 21 = 41
41 divided by 2 = 20.5
Sample Problem (ODD)
Find the lower extreme.
[10, 10, 14, 15,] 17, [20, 20, 21, 22]
Sample Problem (ODD)
The lower extreme is 10.
[10, 10, 14, 15,] 17, [20, 20, 21, 22]
Sample Problem (ODD)
Find the upper extreme.
[10, 10, 14, 15,] 17, [20, 20, 21, 22]
Sample Problem (ODD)
The upper extreme is 22.
[10, 10, 14, 15,] 17, [20, 20, 21, 22]
Sample Problem (ODD)
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= 17
Lower Quartile = 12
Upper Quartile = 20.5
Lower Extreme = 10
Upper Extreme = 22
Sample Problem (ODD)
Find the interquartile range for the set
of data.
[10, 10, 14, 15, 17,20, 20, 21, 22]
Median= 17
Lower Quartile = 12
Upper Quartile = 20.5
Lower Extreme = 10
Upper Extreme = 22
Sample Problem (ODD)
The interquartile range is 8.5.
20.5 – 12 = 8.5
[10, 10, 14, 15, 17,20, 20, 21, 22]
Median= 17
Lower Quartile = 12
Upper Quartile = 20.5
Lower Extreme = 10
Upper Extreme = 22
Sample Problem (ODD)
Find the range of the data set.
[10, 10, 14, 15, 17,20, 20, 21, 22]
Sample Problem (ODD)
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, 20
7 + 8 = 15
15 divided by 2 = 7.5
The median is 7.5
Even Numbered Data Sets
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 = 18
The range for this data set = 18
Even Numbered Data Sets
[ 2, 4, 5, 6, 7] 7.5 [8, 9, 11, 19, 20]
Median = 7.5
Lower Quartile = 5
Upper Quartile = 11
Upper Extreme = 20
Lower Extreme = 2
Any Questions?
Sample Problem
Use the following data set to create a 5
number summary
1,2,3,4,5,6,7,8,9,10,11,12
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 = 3.5
Lower 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 = 12
Lower Extreme = 1
Sample Problem
What is the 5 number summary?
Median = 6.5
Lower Quartile = 3.5
Upper Quartile = 8.5
Upper Extreme = 12
Lower Extreme = 1
Any Questions?