91Ó°ÊÓ

We need to find the components in five-number summary .

The components in five number theory are presented together and ordered from lowest to highest: minimum value, lower quartile $\left(Q1\right)$, median value $\left(Q2\right)$, upper quartile $\left(Q3\right)$, maximum value.

We need to find that how five-number summary can be employed to describe center and variation .

From the three quartiles$(Q1,Q2,Q3Q1,Q2,Q3)$, we can obtain a measure of center (the median,$Q2$) and measures of variation of the two middle quarters of the data, $\left(Q2−Q1\right)$for the second quarter and role="math" localid="1651076738621" $(Q3−Q2)$for the third quarter. But the three quartiles do not tell us anything about the variation of the first and fourth quarters.

.The variation of the first quarter can be measured as the difference between the minimum and the first quartile, $Q1−Min$, and the variation of the fourth quarter can be measured as the difference between the third quartile and the maximum, $Max−Q3$. Thus the minimum, maximum, and quartiles together provide, among other things, information on center and variation.

We need to find what graphical display is based on five-number summary .

Boxplots are a graphical display based upon the five-number summary and are very commonly used to compare the distributions of a quantitative variable for multiple groups.