Chapter 10.5, Problem 18PPS

Solution

a.

Given:

Money spent(boys):114,98,131,83,91,64,94,77,96,105,72,108,87,112,58,126

Money spent(girls):124,74,105,133,85,162,90,109,94,102,98,171,138,89,154,76

Graph:

Money spent (boys):

  

Money spent (girls):

  

Interpretation:

The 1^st graph is relatively skewed while the 2^nd graph is positively skewed.

b.

To compare the data

Boys:

Maximum=131

Minimum=58

Median=95

Lower quartile=77

Upper quartile=112

Girls:

Maximum=171

Minimum=74

Median=103.5

Lower quartile=89

Upper quartile=138

Given information:

Money spent(boys):114,98,131,83,91,64,94,77,96,105,72,108,87,112,58,126

Money spent(girls):124,74,105,133,85,162,90,109,94,102,98,171,138,89,154,76

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:

Boys :

Sortingdata,

58,64,72,77,83,87,91,94,96,98,105,108,112,114,126,131

The 5 number summary is used because, the data can have abnormalities/distortion.

Maximum=131

Minimum=58

Substituting values,

Median is,

  $\frac{{(\frac{N}{2})}^{th}ob+{(\frac{N}{2}+1)}^{th}ob}{2}=\frac{{(\frac{16}{2})}^{th}ob+{(\frac{16}{2}+1)}^{th}ob}{2}=\frac{{(8)}^{th}ob+{(8+1)}^{th}ob}{2}=\frac{{(8)}^{th}ob+{(9)}^{th}ob}{2}=\frac{94+96}{2}=95$

Lower quartile= $\frac{{(N+1)}^{th}ob}{4}=\frac{{(16+1)}^{th}ob}{4}={4.25}^{th}ob$

Removing .25,

Lower quartile= $4^{th}ob=77$

Upper quartile= $\frac{3{(16+1)}^{th}ob}{4}=3\times {4.25}^{th}ob={12.75}^{th}ob$

Adding 0.25,

Upper quartile= ${13}^{th}ob=112$

Girls:

74,76,85,89,90,94,98,102,105,109,124,133,138,154,162,171

Maximum=74

Minimum=171

Substituting values,

Median is,

  $\frac{{(\frac{N}{2})}^{th}ob+{(\frac{N}{2}+1)}^{th}ob}{2}=\frac{{(\frac{16}{2})}^{th}ob+{(\frac{16}{2}+1)}^{th}ob}{2}=\frac{{(8)}^{th}ob+{(8+1)}^{th}ob}{2}=\frac{{(8)}^{th}ob+{(9)}^{th}ob}{2}=\frac{102+105}{2}=103.5$

Lower quartile= $\frac{{(N+1)}^{th}ob}{4}=\frac{{(16+1)}^{th}ob}{4}={4.25}^{th}ob$

Removing .25,

Lower quartile= $4^{th}ob=89$

Upper quartile= $\frac{3{(16+1)}^{th}ob}{4}=3\times {4.25}^{th}ob={12.75}^{th}ob$

Adding 0.25,

Upper quartile= ${13}^{th}ob=138$