Question

The data set shows the number of stamps that each of 10 stamp collectors brought to a show.

71, 84, 133, 140, 158, 166, 170, 171, 188, 198
Which statement is true?
Both 71 and 84 are outliers.
Only 198 is an outlier.
Both 71 and 198 are outliers.
Only 71 is an outlier.

Answer 1

Only 71 is an outlier.

Answer 2

Only 71 is an outlier.

Explanation:

The give data is

71, 84, 133, 140, 158, 166, 170, 171, 188, 198

Divide the data in two equal parts.

(71, 84, 133, 140, 158), (166, 170, 171, 188, 198)

Now, divide each parenthesis in two equal parts.

(71, 84), 133, (140, 158), (166, 170), 171, (188, 198)

It means first quartile is 133 and third quartile is 171.

The interquartile range is

`IQR=Q_3-Q_1=171-133=38`

If the data lies outside the range
`[Q_1-1.5(IQR),Q_3+1.5(IQR)]`, then the data set has outliers.

`[Q_1-1.5(IQR),Q_3+1.5(IQR)]=[133-1.5(38),171+1.5(38)]`

`[Q_1-1.5(IQR),Q_3+1.5(IQR)]=[76,228]`

It means if the data lies outside the interval [76,228], then it is an outlier.

Since 71∉[76,228], therefore only 71 is an outlier.