Chapter 10.3, Problem 22PFA

a.

To determine

To find minimum, lower quartile, median, upper quartile and maximum.

Answer to Problem 22PFA

Minimum is 1215, Lower quartile is 2060, Median is 1518, Upper quartile is 1342 and Maximum is 2788

Explanation of Solution

Given information:

Rank	Gross(million $)	Rank	Gross(million $)
1	2788	6	1516
2	2187	7	1405
3	2060	8	1342
4	1670	9	1277
5	1520	10	1215

Formula used:

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

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

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

Where N is number of tiles/data points

Calculation:

Minimum is the smallest value in the data set. Hence, substituting the value,

  $Minimum=1215$

Maximum is the highest value in the data set. Hence, substituting the value,

  $Maximum=2788$

For median substituting values,

  $=\frac{(\frac{{10}^{th}}{2})ob+{(\frac{10}{2}+1)}^{th}ob}{2}$

On solving,

  $=\frac{5^{th}ob+6^{th}ob}{2}$

On substituting the value,

  $=\frac{1520+1516}{2}$

On solving,

  $median=1518$

For Lower quartile substituting the value,

  $=\frac{{(10+1)}^{th}}{4}ob$

On solving,

  $=2.75$

On rounding off,

  $\approx 3^{rd}ob$

Substituting the value,

  $LowerQuartile=2060$

Hence, the lower quartile is 2060

For Upper quartile substituting the value,

  $=\frac{3{(10+1)}^{th}}{4}ob$

Solving,

  $=8.25$

On rounding off,

  $\approx 8$

Substituting the value,

  $UpperQuartile=1342$

Hence, Minimum is 1215, Lower quartile is 2060, Median is 1518, Upper quartile is 1342 and Maximum is 2788

b.

To determine

To interpret 5 number summary

Answer to Problem 22PFA

Five number summary is 1215, 2060, 1518, 1342, 2788

Explanation of Solution

Given information: Minimum is 1215, Lower quartile is 2060, Median is 1518, Upper quartile is 1342 and Maximum is 2788

Rank	Gross(million $)	Rank	Gross(million $)
1	2788	6	1516
2	2187	7	1405
3	2060	8	1342
4	1670	9	1277
5	1520	10	1215

The five number summary consists of minimum, lower quartile, median, upper quartile and maximum.

Hence, substituting the values,

Five number summary is 1215, 2060, 1518, 1342, 2788