Question

Which statement is true about this data set? {79, 66, 82, 83, 84, 86, 85, 84, 84, 85, 88}

88 is an outlier because it is greater than the upper fence.

66 and 88 are both outliers because 66 is less than the lower fence and 88 is greater than the upper fence.

This data set has no outliers.

66 is an outlier because it is less than the lower fence

Answer 1

66 is the outlier because it is less than all the other numbers while all the numbers are in the 70s and 80s

Answer 2

Option 4 is true as 66 is an outlier because it is less than the lower fence.

Explanation:

Given : The data {79, 66, 82, 83, 84, 86, 85, 84, 84, 85, 88}

To find : Which statement is true about this data set?

Solution :

The statements is all about outlier.

So, we find the outlier of the data.

Step 1- Arranging the data from lowest to highest,

{66,79, 82, 83, 84, 84, 84, 85, 85, 86, 88}

Step 2 - Find the median of the data

As the data is odd numbers so the median is
`(n+1)/(2)` th term.

`(n+1)/(2)=(11+1)/(2)=6th` term.

6th term is 84 ⇒ Median =84

Step 3 - To find Upper quartile and lower quartile

Lower quartile data set is the median of the upper terms from median

{66,79, 82, 83, 84}

Median of the set is 82

∴
`Q_1=82`

Upper quartile data set is the median of the lower terms from median

{ 84, 85, 85, 86, 88}

Median of the set is 85

∴
`Q_3=85`

Step 4 - To find the interquartile range.

`\text{IQR}=Q_3-Q_1`

`\text{IQR}=85-82=3`

Step 5 - To find the fences for the data set.

The formula to find range is

`[Q_1-1.5(\text{IQR}),Q_3+1.5(\text{IQR})]`

Substitute the values, we get

`[82-1.5(3),85+1.5(3)]`

`[82-4.5,85+4.5]`

`[77.5,89.5]`

So, All the data lies in the range and the number which don't lie in the range is the outlier of the data.

Therefore, In the given data 66 is the number not lies in the range.

Hence, option 4 is correct or true as 66 is an outlier because it is less than the lower fence.