91Ó°ÊÓ

We are given that,

The data set for maximum wind speed is,
$x_i=85,80,100,115,110,90,80,90,105,115$

No. of values are,

$N=10$

We know that,

The mean is given as,

$$\begin{gathered} \mathrm{μ}=\frac{{\displaystyle \underset{}{∑}}{x}_i}{N} \\ =\frac{85+100+110+80+105+80+115+90+115}{10} \\ =\frac{970}{10}=97 \end{gathered}$$

We need to find out the standard deviation.

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

Now, the sum of squared deviations is, $\underset{}{\overset{}{∑}}{\left(x_i-\mathrm{μ}\right)}^2=144+9+169+289+64+289+324+49+49+324=1710$

Therefore, the Standard deviation is,

$\mathrm{σ}=\sqrt{\frac{\underset{}{\overset{}{∑}}{\left(x_i-\mathrm{μ}\right)}^2}{N}}=\sqrt{\frac{1710}{10}}=\sqrt{171}≈13.0767$

We need to find out the median of the data

Data in the ordered list is,

$80,80,85,90,90,100,105,110,115,115$

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

Therefore, median is,

$\mathrm{η}=\frac{90+100}{2}=95$

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,$80,90,115$

We need to find the value of IQR

As we know,

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

Therefore,$Q_1=85$

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

Therefore, $Q_3=110$

Hence, the interquartile range is,

$IQR=Q_3-Q_1=110-85=25$