Chapter SH, Problem 13.3.2EP

To determine

To find:the range, interquartile range, and any outliers for the given data

Answer to Problem 13.3.2EP

The range is $170$ , the inter quartile range is $607.5$ and here outliers are $\text{none }$

Explanation of Solution

Given:

  $271,891,181,193,711,791,861,818$

Calculation:

Range:

Order the data from least to greatest.

  $271,891,181,193,711,791,861,818$

Range is the difference between greatest and smallest value.

  $\begin{array}{l}\text{Range}=891-181\\ =710\end{array}$

Hence, the range is $710$ .

Inter quartile range:

Find the upper quartile and lower quartile.

Here median is $\frac{711+791}{2}=751$

Divide the data into two halves.

  $\stackrel{\text{Upper half}}{\overbrace{181,193,271,711,}}\stackrel{\text{median}}{\overbrace{751,}}\stackrel{\text{Upper half}}{\overbrace{791,818,861,891}}$

Median of lower half is

  $\begin{array}{l}LQ=\frac{193+271}{2}\\ =232\end{array}$

Median of upper half is

  $\begin{array}{l}\text{UQ}=\frac{818+861}{2}\\ 839.5\end{array}$

Inter quartile range is

  $\begin{array}{l}\text{UQ}-\text{LQ}=839.5-232\\ =607.5\end{array}$

Hence, the inter quartile range is $607.5$

OutlierData that are more than 1.5 times the value of the interquartile range beyond the quartiles is called outlier.

Here inter quartile range is 607.5

  $607.5\times 1.5=911.25$

Now subtract 911.25 from the lower quartile and add to upper quartile.

  $\begin{array}{l}\text{LQ}-911.25=-679.25\hfill \\ \text{UQ}+911.25=1750.75\hfill \end{array}$

Thus the data which is not in the range of -679.25 to 1750.75 is outlier.

Here outliers are $\text{none }$

Conclusion:

Therefore, the range is $170$ , the inter quartile range is $607.5$ and here outliers are $\text{none }$