Check the following data set for outliers. 73, 82, 84, 84, 86, 87, 89, 91
Solution:
73 is an outlier:
Explanation:
Any value below
Q1-1.5IQR
and any value above
Q3 +1.5 IQR is an outlier
where Q1 is first quartile and Q3 is third quartile and IQ=interquartile range=Q3-Q1
The first quartile of the data set is 83.
Explanation
The first quartile (or lower quartile or 25th percentile) is the median of the bottom half of the numbers. So, to find the first quartile, we need to place the numbers in value order and find the bottom half.
73 82 84 84 86 87 89 91
So, the bottom half is
73 82 84 84
The median of these numbers is 83.
So first quartile=83
The third quartile of the data set is 88.
Explanation
The third quartile (or upper quartile or 75th percentile) is the median of the upper half of the numbers. So, to find the third quartile, we need to place the numbers in value order and find the upper half.
73 82 84 84 86 87 89 91
So, the upper half is
86 87 89 91
The median of these numbers is 88.
So third quartile is 88
he interquartile range of the data set is 5.
Explanation
The interquartile range is the difference between the third and first quartiles.
The third quartile is 88.
The first quartile is 83.
The interquartile range = 88 - 83 = 5.
lower fence=Q1-1.5(IQR)=83-1.5*5=75.5
upper fence=Q3+1.5(IQR)=88+1.5*5=95.5
73 is an outlier since 73<75.5(lower fence)
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