Q. 12 - Elementary Statistics

Question

Regarding the five-number summary:
a. Identify its components.
b. How can it be employed to describe center and variation?
c. What graphical display is based on it?

Step-by-Step Solution

Answer

a. The components are minimum value, lower quartile , median value , upper quartile , maximum value. 

b. The center and variation can found by three quartiles ,$Q_1-Min$,$Max-Q_3$

c. The graphical display is based on it is boxplots.

Part(a) Step 1: Given information

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

Part(a) Step 2: Explanation

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. 

Part(b) Step 1: Given information

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

Part(b) Step 2: Explanation

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 $(Q3-Q2)$ 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.

Part(c) Step 1: Given information

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

Part(c) Step 2: Explanation

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.