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Check the following data set for outliers. 73, 82, 84, 84, 86, 87, 89, 91

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Check the following data set for outliers. 73, 82, 84, 84, 86, 87, 89, 91

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Answer #1

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)


answered by: gavin
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