Chapter 10.4, Problem 9PPS

To determine

To describe the center and represent data as dot plot

Answer to Problem 9PPS

Maximum=61

Minimum=44

Median=53

Lower quartile=49

Upper quartile=55

Explanation of Solution

Given information:

Temperature (℉)
48	50	55	53	57	53	44	61	57	49	51	58	56	54	57
50	55	47	57	48	58	53	49	56	59	52	48	55	53	51

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,

44,47,48,48,48,49,49,50,50,51,51,52,53,53,53,53,54,55,55,55,56,56,57,57,57,57,58,58,59,61

Maximum=61

Minimum=44

Substituting values,

Median= $\frac{{(\frac{30}{2})}^{th}ob+{(\frac{30}{2}+1)}^{th}ob}{2}=\frac{{(15)}^{th}ob+{(16)}^{th}ob}{2}=\frac{53+53}{2}=53$

Lower quartile= $\frac{{(30+1)}^{th}ob}{4}={6.25}^{th}ob$

Removing .25,

Lower quartile= $6^{th}ob=49$

Upper quartile= $\frac{3{(30+1)}^{th}ob}{4}=3\times {6.25}^{th}ob={18.75}^{th}ob$

Adding 0.25,

Upper quartile= ${19}^{th}ob=55$

Graph:

Minimum:44

Maximum:61