Question

1.What is the interquartile range of the following data set?5, 6, 7, 3, 4, 5, 6, 8, 7562.50.5

Answer 1

Given:

The data set is 5,6,7,3,4,5,6,8,7.

The objective is to find the interquartile range of the set.

The number of values in the set is N = 9.

Then, the median can be calculated as,

`\begin{gathered} \text{Median}=(N+1)/(2) \\ =(9+1)/(2) \\ =5th\text{ term} \end{gathered}`

In the given data set, the 5th term is 4. Thus the median of the data set is 4.

Then, the lower half of the data set is on the left side of the median, which is 5,6,7,3.

Similarly, the upper half of the data set is on the right side of the median, which is 5,6,8,7.

The formula to find the interquartile is,

`IQR=Q_3-Q_1\ldots\ldots(1)`

To find the value of Q1, find the mid term from the lower half of the data set.

`\begin{gathered} Q_1=(6+7)/(2) \\ =(13)/(2) \\ =6.5 \end{gathered}`

To find the value of Q2, find the mid term from the upper half of the data set.

`\begin{gathered} Q_3=(6+8)/(2) \\ =(14)/(2) \\ =7 \end{gathered}`

On plugging the value of Q1 and Q3 in equation (1),

`\begin{gathered} \text{IQR}=7-6.5 \\ =0.5 \end{gathered}`

Thus, the interquatile range is 0.5.

Hence, option (4) is the correct answer.