Chapter 10.4, Problem 7PPS

To determine

To describe the centre and spread of data.

Answer to Problem 7PPS

5-number summary.

Explanation of Solution

Given information:

32,44,50,49,21,12,27,41,48,30,50,23,37,16,49,53,33,25,35,40,48,39,50,24,15,29,37,50,36,43,49,44,46,27,42,47

Formula used:

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

Medium quartile=$\frac{(N+1)}{2}$

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

Where N is number of tiles/data points

Calculation:

Sorting data,

12,15,16,21,23,24,25,27,27,29,30,32,33,35,36,37,37,39,40,41,42,43,44,44,46,47,48,48,49,49,49,50,50,50,50,53

Total data points=36

The 5 number summary is used because, the total data is too big to calculate for mean and standard deviation.

Maximum=53

Minimum=12

Median$\frac{{(\frac{N}{2})}^{th}+{(\frac{N}{2}+1)}^{th}ob}{2}=\frac{(\frac{36}{2})+(\frac{36}{2}+1)}{2}=\frac{{18}^{th}ob+{19}^{th}ob}{2}=39.5$

Pair these 18^th and 19^th term. Lower half has lower quartile and upper half has upper quartile,

Data point in lower half=17

Lower quartileLower quartile=${(\frac{N+1}{2})}^{th}ob$=9thob=27

Data point in upper half=17

Upper quartile=${(\frac{N+1}{2})}^{th}ob$=9thob=48

Upper quartile=${(\frac{N+1}{2})}^{th}ob$=9thob=48

Graph: