Chapter 13, Problem 7PT

To determine

The percent of data shown by below $21$ by using the following set of data:

$15$	$19$	$26$	$14$	$17$
$13$	$20$	$21$	$29$	$18$

Answer to Problem 7PT

The percent of data shown by below $21$ is $75\%$

Explanation of Solution

Given:

$15$	$19$	$26$	$14$	$17$
$13$	$20$	$21$	$29$	$18$

Concept Used:

The given set of data dividing into the four equal parts is known as quartile. the division of the set of data is to be arranged in the quartile form only after arrangement in the ascending order.

The upper and lower quartile is referred to as lower and highest quartile.

Calculation:

Arrange the given from least to highest:

  $13,14,15,17,18,19,20,21,26,29$

Now, calculate median of the above numbers system:

It is even number system so take the mean of middle two numbers as median:

  $\begin{array}{l}X=\frac{18+19}{2}\\ X=18.5\end{array}$

Now, find the lower quartile by using the median of the lower set of data $13,14,15,17,18$ . This lowers set of data is odd so, the median is $15$ .

Now, find the upper quartile by using the median of the upper set of data $19,20,21,26,29$ . This upper set of data is odd so, the median is $21$ .

  

Since, $21$ is the upper quartile, so it represents $75\%$ of the data.

Conclusion:

Hence, upper and lower quartile is used to calculate the percent of data.