Chapter 14.3, Problem 1CFU

To determine

To calculate: The quartile points, inter-quartile range, semi-inter-quartile range, and any outliers.

Answer to Problem 1CFU

Quartile points are $Q_1=60,Q_2=70,Q_3=100.$

Outliners are $170\text{ and 180}\text{.}$

Interquartile range is $40$ .

Semi- interquartile range is $20.$

Explanation of Solution

Given information:

  

Formula used:

If each group has the median, the data is divided into four groups. Each group is called quartile.

The difference between the first quartile point and third quartile point is called the inter- quartile range.

The inter- quartile range is divided by 2, the quotient is called the semi- interquartile range.

Outliers are extreme values that are more than 1.5 times the inter-quartile range beyond the upper or lower quartiles. Quartiles are represented by single points.

Calculation:

Consider Box-and-whisker plots ,

The quartile points are :-

  $\begin{array}{l}{Q}_1=60\\ Q_2=70\\ Q_3=100\end{array}$

The lower extreme is $40$ and the upper extreme is $140.$

The outliers are $170\text{ and 180}\text{.}$

The inter- quartile range is $Q_3-Q_1.$

  $\begin{array}{l}=100-60\\ =40\end{array}$

The semi-interquartile range -

  $\frac{\text{inter-quartile range}}{2}.$

  $\begin{array}{l}=\frac{40}{2}\\ =20.\end{array}$

Hence, the Quartile points are $Q_1=60,Q_2=70,Q_3=100.$ The outliners are $170\text{ and 180}\text{.}$

  $$ The interquartile range is $40$ and semi- interquartile range is $20.$