Question

Which statement is true about this data set?

{70, 67, 66, 65, 66, 78, 68, 71, 80, 78, 72}



65 is an outlier because it is less than the lower fence.

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

This data set has no outliers.

65 and 80 are both outliers because 65 is less than the lower fence and 80 is greater than the upper fence.

Answer 1

Option 3 - This data set has no outliers.

Explanation:

Given : The data {70, 67, 66, 65, 66, 78, 68, 71, 80, 78, 72}

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,

{65,66,66,67,68,70,71,72,78,78,80}

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 70 ⇒ Median =70

Step 3 - To find Upper quartile and lower quartile

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

{65,66,66,67,68}

Median of the set is 66

∴
`Q_1=66`

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

{71,72,78,78,80}

Median of the set is 78

∴
`Q_3=78`

Step 4 - To find the interquartile range.

`IQR=Q_3-Q_1=78-66=12`

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

`[66-1.5(12),78+1.5(12)]`

`[66-18,78+18]`

`[48,96]`

The range in which data lies is [48,96]

We have seen that all the data lie inside the range.

Therefore, This data set has no outliers.

Hence, Option 3 is correct.