Question

The interquartile range of the data set is 4. 2,2,3,3,4,5,5,6,7,9,12 which explains whether or not 12 is an outlier?

Answer 1

Answer:

12 is not an outlier because it is near by to the boundaries.

Step-by-step explanation:

Given : The interquartile range of the data set is 4. Data is 2,2,3,3,4,5,5,6,7,9,12.

To find : Whether or not 12 is an outlier?

Solution :

Data 2,2,3,3,4,5,5,6,7,9,12

There are 11 terms so median of the data is 6th term.

Median = 5

The lower quartile from 2,2,3,3,4

Median is 3 so, $Q_1=3$

The upper quartile from 5,6,7,9,12

Median is 7 so, $Q_3=7$

Interquartile is $Q_3-Q_1=7-3=4$

Inner fence of the data is

First we find $IQR\times 1.5=4\times 1.5=6$

Then, subtract the number from first quartile

3-6=-3

And Add the number to third quartile

7+6=13

Inner fence boundaries are -3 and 13.

Outer fence of the data is

First we find $IQR\times 3=4\times 3=12$

Then, subtract the number from first quartile

3-12=-9

And Add the number to third quartile

7+12=19

Inner fence boundaries are -9 and 19.

Outliers are number that are way out of the boundaries set in both the inner and outer fence.                                

12 is not an outlier because it is near by to the boundaries.