Chapter 10.4, Problem 6PPS

To determine

To graph a box and whisker plot of the given data set

Explanation of Solution

Given information: Data set is

45, 17, 16, 22, 25, 19, 20, 21, 32, 37, 19, 21, 24, 20, 18, 22, 23, 19.

Formula used:

Lower quartile is,

  $Q1=(n+1)\frac{1}{4}term$

Upper quartile is,

  $Q3=(n+1)\frac{3}{4}term$

Median is,

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

Graph:

  

Calculation:

Re-arranging the data in ascending order,

33, 36, 37, 39, 40, 40, 42, 43, 43, 43, 44, 45, 46, 46, 46, 47, 47, 48, 48, 48, 49, 50, 50, 50, 50, 51, 51, 51, 51, 51, 52, 52, 53, 54, 54, 55

For median, substituting the values,

  $M=\frac{(\frac{36}{2})+(\frac{36}{2}+1)}{2}term$

On solving,

  $M=\frac{{18}^{th}+{19}^{th}}{2}term$

Substituting the values,

  $M=\frac{48+48}{2}$

On solving,

  $M=48$

Hence, median and Q2 is 48

For lower quartile, substituting the values,

  $Q1=(36+1)\frac{1}{4}$

On solving,

  $Q1=9.25$

Rounding off the value,

  $Q1\approx 9$

Substituting the value,

  $Q1=43$

Hence, lower quartile is 43

For upper quartile substituting the values,

  $Q3=(36+1)\frac{3}{4}$

On solving,

  $Q3=27.75$

On rounding off,

  $Q3\approx 28$

Substituting the value,

  $Q3=51$

Hence, upper quartile is 51

Minimum is the smallest value of the data set.

Hence, minimum is 33

Maximum is the biggest value of the data set.

Hence, maximum is 55

Hence, the five- number summary is 33, 43, 48, 51, 55.

Hence, box-whisker plot is