Chapter 10.4, Problem 4CYU

To determine

To describe the center and spread of data and construct box-and-whisker plot

Answer to Problem 4CYU

Maximum=21

Minimum=6

Median=17

Lower quartile=10

Upper quartile=19

Explanation of Solution

Given information:

Data set: 20,18,15,17,18,,10,15,10,18,19,17,19,12,6,19,15,21,10,9,18

Formula used:

Lower quartile= $\frac{(N+1)}{4}$

Median= $\frac{{(\frac{N}{2})}^{th}ob+{(\frac{N}{2}+1)}^{th}ob}{2}$

Upper quartile= $\frac{3(N+1)}{4}$

Where N is number of tiles/data points

Calculation:

Sorting data,

6,9,10,10,10,12,15,15,15,17,17,18,18,18,18,19,19,19,20,21

Maximum=21

Minimum=6

Substituting values,

Median $=\frac{{(\frac{20}{2})}^{th}ob+{(\frac{20}{2}+1)}^{th}ob}{2}=\frac{{(10)}^{th}ob+{(11)}^{th}ob}{2}=\frac{17+17}{2}=17$

Lower quartile= $=\frac{{(20+1)}^{th}ob}{4}={5.25}^{th}ob$

Removing .25,

Lower quartile= $5^{th}ob=10$

Upper quartile= $\frac{3{(20+1)}^{th}ob}{4}=3\times {5.25}^{th}ob={15.75}^{th}ob$

Adding 0.25,

Upper quartile= ${16}^{th}ob=19$

Graph:

  

Interpretation:

Data is negatively skewed.