Question

What is the Interquartile Range for the following data set? (5,6,7,3,9,8,3,1,6,7,7)

Answer 1

Sorting, we have 1 3 3 5 6 6 7 7 7 8 9. The middle number is 6. The lower quartile is 3. The upper is 7. 7-3=4.

Answer 2

Answer:

$IQR=4$

Step-by-step explanation:

We have been given a data set and we are asked to find the Interquartile Range for our given data set.

Since we know that IQR is the difference between upper quartile and lower quartile, so we need to find $Q_3\text{ and }Q_1$ for our given data set.

First of all let arrange data points of our given data set in ascending order.

1, 3, 3, 5, 6, 6, 7, 7, 7, 8, 9.

$Q_1=(\frac{n+1}{4})^{\text{th value}}$, where n represents total number of data points.

$Q_1=(\frac{11+1}{4})^{\text{th value}}$

$Q_1=(\frac{12}{4})^{\text{th value}}$

$Q_1=(3)^{\text{th value}}$

Since 3rd data point of our given data set is 3, so lower quartile of our data set is 3.

$Q_3=(\frac{3(n+1)}{4})^{\text{th value}}$, where n represents total number of data points.

$Q_3=(\frac{3(11+1)}{4})^{\text{th value}}$

$Q_3=(\frac{3(12)}{4})^{\text{th value}}$

$Q_3=(3*3)^{\text{th value}}$

$Q_3=(9)^{\text{th value}}$

Since 9th data point of our given data set is 7, so upper quartile of our data set is 7.

$IQR=Q_3-Q_1$

$IQR=7-3$

$IQR=4$

Therefore,interquartile range for our given data set is 4.