Question

How do you find the range and interquartile range of 2, 4, 8, 3 and 2?

Answer 1

Hint: To obtain the range and interquartile of the data given we will use the formula of range and interquartile. Firstly arrange the given data in ascending order then subtract the lowest value from the highest value for obtaining the range. Then for finding the interquartile range find the first second and third quartile then subtract the first quartile from the third quartile to get the desired answer.

Complete step-by-step solution:
The data set is given as:
$2,4,8,3,2$
Firstly we will arrange them in ascending order as,
$2,2,3,4,8$
Now for calculating the range we will subtract the lowest value from the highest value as:
Range $=8-2$
Range $=6$
Now, for finding the interquartile range $\left( IQR \right)$ we will find the Quartile 1 $\left( Q1 \right)$, Quartile 2 $\left( Q2 \right)$, and Quartile 3 $\left( Q3 \right)$ as below:
So as we know Quartile 2 is equal to the median of the data and median of the above data will be
$2,2,\underline{3},4,8$
Median$=3$
$Q2=3$…..$\left( 1 \right)$
Next the Q1 is the middle term of the first half of the data so the first half of the data is:
$\begin{align}
  & \underline{2,2},3,4,8 \\
 & \text{ }\uparrow \\
\end{align}$
So the first half of the data has two terms
$Q1=\dfrac{2+2}{2}$
$\therefore Q1=2$……$\left( 2 \right)$
Next the Q3 is the middle term of the second half of the data so the second half of the data is:
$\begin{align}
  & 2,2,3,\underline{4,8} \\
 & \text{ }\uparrow \\
\end{align}$
$Q3=\dfrac{4+8}{2}$
$\therefore Q3=6$……$\left( 3 \right)$
On subtracting equation (2) from equation (3) we get,
$\begin{align}
  & IQR=6-2 \\
 & \therefore IQR=4 \\
\end{align}$
Hence the range and interquartile range of the data given is 6 and 4 respectively.

Note: The range is the distance from the highest value to the lowest value of the data. The interquartile range is the distance from the highest quartile to the lowest quartile of a data. Interquartile is used to find how the data points are spread out from the mean in a set.