To identify the ouliers we can use the Interquartile Range (IQR).
1. To find the IQR, we need to have the data set in order:
74, 75, 78, 79, 80, 81, 82, 84, 84, 87.
2. Find the median:
As we have an even set of numbers, just place a mark in the center of the data set:
74, 75, 78, 79, 80 | 81, 82, 84, 84, 87
3. Place parentheses around the numbers above and below the mark we just made:
(74, 75, 78, 79, 80) | (81, 82, 84, 84, 87)
4. Find the median in each group, it would be Q1 and Q3:
(74, 75, 78, 79, 80) | (81, 82, 84, 84, 87)
Q1=78 and Q3=84
5. Subtract Q1 from Q3:
Q3-Q1=84-78=6
This is the IQR: 6.
6. Multiply the IQR by 1.5:
IQR*1.5 = 6*1.5 = 9
7. Subtract this value from Q1:
Q1-9= 78-9 = 69 This is the lower limit
8. Add the value to Q3:
Q3+9= 84+9 = 93 This is the upper limit
Identify the numbers that are under the lower limit and above the upper limit, those are the outliers.
As you can see, in the data set there are not outliers.