Question

The data set represents the number of rings each person in a room is wearing. 0, 2, 4, 0, 2, 3, 2, 8, 6 What is the interquartile range of the data?

Answer 1

Interquartile Range = 4

Explanation:

To find Inter Quartile Range (IQR) first we arrange the data set in ascending order to get Median.

0, 0, 2, 2, 2, 3, 4, 6, 8

In this data Median is the middle number "2"

Now we calculate Lower quartile

0, 0, 2, 2, 2, 3, 4, 6, 8

Find the median of left side data values of the median, there are two middle numbers so we take the mean

=
`(0 + 2)/(2)` = 1

Now calculate upper quartile

The median of right side data values of the median is called upper quartile, there are two middle numbers 4 & 6 so we take the mean

=
`(4 + 6)/(2)` = 5

Inter Quartile Range = Upper quartile - Lower quartile

IQR = 5 - 1 = 4

Answer 2

`IQR=4`

Explanation:

We have been given a data set that represents the number of rings each person in a room is wearing as: 0, 2, 4, 0, 2, 3, 2, 8, 6. We are asked to find the interquartile range of the data.

Let us arrange our data points from least to greatest order.

0, 0, 2, 2, 2, 3, 4, 6, 8.

Let us find median of our data set. Since our data set has 9 data points, therefore, median of our given data set will be value of 5th term, that is 2.

Now let us find lower quartile, which is also known as the median of the data points to the left of median.

We have 4 data points to the left of our median, so our lower quartile will be average of 2nd and 3rd data point.

`Q_1=(0+2)/(2)=(2)/(2)=1`

Now let us find upper quartile of our given data set, which is the median of the data points to the right of median.

We have 4 data points to the right of the median, so our upper quartile will be the average of 7th and 8th data point.

`Q_3=(4+6)/(2)=(10)/(2)=5`

Since we know that interquartile range is the difference between upper and lower quartile.

`IQR=Q_3-Q_1`

`IQR=5-1`

`IQR=4`

Therefore, IQR of our given data set is 4.