Chapter 10.4, Problem 3CYU

To determine

To describe the centre and spread of data.

Answer to Problem 3CYU

5-number summary.

Explanation of Solution

Given information: 58,66,52,75,60,56,78,63,59,54,60,67,72,80,68,88,55,60,59,61,82,70,67,60,58,86,74,61,92,76,58,62,

66,74,69,64

Formula used:

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

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

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

Where N is number of tiles/data points

Calculation:

Sorting data,

52,54,55,56,58,58,58,59,59,60,60,60,60,61,61,62,63,64,66,66,67,67,68,69,70,72,74,74,75,76,78,80, 82,86,88,92

Total data points=35

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

Maximum=92

Minimum=52

Median= $\frac{{(N+1)}^{th}ob}{2}=\frac{(35+1)}{2}={18}^{th}ob=64$

Lower quartile= $\frac{(N+1)}{4}$ = $\frac{(N+1)}{2}=\frac{35+1}{4}=9^{th}ob=59$

Upper quartile= $\frac{3\times (N+1)}{4}=\frac{3(35+1)}{4}={27}^{th}ob=74$

Graph: