91Ó°ÊÓ

We are given that,

The data set is, $$\begin{gathered} x_i=25,24,31,36,23,32,23,25,27,30,28,38,23,20,21,35,24,25, \\ 23,35,25 \end{gathered}$$

No. of values are,

$N=21$

We know that,

The mean is given as,

We need to find out the standard deviation.

We know that the standard deviation is the square root of variance which is given as,

The standard deviation is,

$\mathrm{σ}=\sqrt{\frac{Total}{N}}=\sqrt{\frac{562.2857}{21}}=5.1745$

We need to find out the median of the data

Data in the ordered list is,

$$\begin{gathered} 20,21,23,23,23,23,24,24,25,25,25,25,27,28,30,31,32,35,35, \\ 36,38 \end{gathered}$$

The median of the sorted list is the middle value of the list,

Therefore, median is,$\mathrm{η}=25$

We need to find out the mode of given data.

We know that mode is the most occurring value in the data set.

Therefore, mode is,$23,25$

We need to find the value of IQR

As we know,

The first quartile is the median of data below the median,

Therefore,$Q_1=\frac{23+23}{2}=23$

And the third quartile is the median of data above median,

Therefore,$Q_3=\frac{31+32}{2}=31.5$

Hence, the interquartile range is,

$IQR=Q_3-Q_1=31.5-23=8.5$