Chapter 10, Problem 22SGR

To determine

To calculate the 5 number summary and construct box and whisker plot

Answer to Problem 22SGR

5 number summary is,

180, 288, 354.5, 383, 432

Explanation of Solution

Given information:

Gallons of milk sold per day,

383, 296, 354, 288, 195, 372, 421, 367, 411, 355, 296, 321, 403, 357, 432, 229, 180, 266

Formula used:

Minimum is,

  $\min =smallestValue$

Maximum is,

  $\max =biggestValue$

Lower quartile is,

  $q1=\frac{1}{4}(n+1)$

Upper quartile is,

  $q3=\frac{3}{4}(n+1)$

Median is,

  $M=\frac{{(\frac{n}{2})}^{th}+{(\frac{n}{2}+1)}^{th}}{2}$

Graph:

Box- and- whisker plot is,

  

Calculation:

Rearranging the values in ascending order,

180, 195, 229, 266, 288, 296, 296,321, 354, 355, 357, 367, 372, 383, 403, 411, 421, 432,

For the minimum, substituting the values,

  $\min =180$

Hence, minimum is 180.

For the maximum, substituting the values,

  $\max =432$

Hence, maximum is 432.

For median, substituting the values,

  $M=\frac{{(\frac{18}{2})}^{th}+{(\frac{18}{2}+1)}^{th}}{2}$

On solving,

  $M=\frac{9^{th}+{10}^{th}}{2}$

Substituting the values,

  $M=\frac{354+355}{2}$

On solving,

  $M=354.5$

Hence, median is 354.5

For lower quartile, substituting the values,

  $q1=\frac{1}{4}(18+1)$

On solving,

  $q1=4.75$

Rounding off,

  $\approx 5^{th}$

Substituting the value,

  $q1=288$

Hence, lower quartile is 288.

For upper quartile, substituting the values,

  $q3=\frac{3}{4}(18+1)$

On solving,

  $q3=14.25$

Rounding off,

  $\approx {14}^{th}$

Substituting the value,

  $q3=383$

Hence, upper quartile is 383.

Therefore the five-number summary is

180, 288, 354.5, 383, 432

5-number summary is chosen, because its best for a grouped data and the values do not change if the data is skewed.