Interquartile Range, Outliers, and Reading Box and Whiskers
How do you find the range for a set of data?
Interquartile Range (IQR) is the range of the middle half of a set of numbers.
IQR = 3rd Q – 1st Q
Examples: Find the IQR of the following:
1st = 65 1st = 70 1st = 30
2nd = 68 2nd = 80 2nd = 40
3rd = 71 3rd = 81.5 3rd = 50
Outliers are data that are more than 1.5 times the interquartile range from the quartiles.
Steps to finding outliers: Example:
44, 37, 23, 35, 190, 61, 95, 95,49, 96 23, 35, 37, 44 49, 61, 95, 95, 96, 190
1. Find the 2nd quartile.
2. Find the 1st quartile.
3. Find the 3rd quartile.
4. Find the interquartile range.
5. Multiply the IQR by 1.5 to find the limit
6. Subtract the limits from the 1st quartile to find the extremes.
7. Add the limit to the 3rd quartile to find the extremes.
2nd = 49 + 61 = 110 ÷ 2 = 55
1st = 37
3rd = 95
IQR = 95 – 37 = 58
58(1.5) = 87
37-87 = -50
95 + 87 = 182
Question?
On the box and whiskers graph below which section contains the most amount of data? (****THIS IS A TRICK QUESTION!!! THINK ABOUT HOW YOU CREATE A BOX AND WHISKERS GRAPH.)
Insert Box and Whiskers Graph
Examples:
Insert Box and Whiskers Graph
Which statement is untrue about the graph above:
a. section a = section d
b. section c = section b
c. sections a, b & c = section d.
d. sections b & c = sections a & d
e. sections a & b = sections b & c
Insert Box and Whiskers Graph
Which statements are true about the graph above:
a. section a = section d
b. section c = section b
c. sections a, b &c = section d.
d. sections b & c = sections a & d
e. sections a & b = sections b & c