Question

Which statement is true about this data set?

Answer 1

Answer:

Option 3 - This data set has no outliers.

Step-by-step 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 $\frac{n+1}{2}$ th term.

$\frac{n+1}{2}=\frac{11+1}{2}=6th$ 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.

Answer 2

The data set has no outliers