Chapter 10.4, Problem 3GP

To determine

To describe the center and spread the data using five-number summary.

Answer to Problem 3GP

The five number summary is 2, 17, 23.5, 26, 32

Explanation of Solution

Given information: Given data is,

19, 2, 25, 14, 24, 20, 27, 30, 14, 25, 19, 32, 21, 31, 25, 16, 24, 22, 29, 6, 26, 32, 17, 26, 24, 26, 32, 10, 22, 19, 26, 24, 11, 23, 19, 8

Formula used: Median is,

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

Lower quartile is,

  $Q1=(n+1)\frac{1}{4}$

Upper quartile is,

  $Q3=(n+1)\frac{3}{4}$

Graph:

  

Calculation:

Re-arranging the data in an ascending order,

2, 6, 8, 10, 11, 14, 14, 16, 17, 19, 19, 19, 19, 20, 21, 22, 22, 23,24, 24, 24, 24, 25, 25, 25, 26, 26, 26, 26, 27, 29, 30, 31,32, 32, 32,

For median substituting the values,

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

On solving,

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

Substituting the values,

  $M=\frac{23+24}{2}$

On solving,

  $M=23.5$

Hence, Median is 23.5

For lower quartile,

Substituting the values,

  $Q1=(36+1)\frac{1}{4}$

So,

  $Q1=37\times \frac{1}{4}$

On solving,

  $Q1=9.25$

On rounding off,

  $\approx 9$

Substituting the value,

  $Q1=17$

Hence, Lower quartile is 17

For higher quartile substituting the values,

  $Q3=(36+1)\frac{3}{4}$

So,

  $Q3=37\times \frac{3}{4}$

On solving,

  $Q3=27.75$

On rounding off,

  $\approx 28$

Substituting the value,

  $Q3=26$

Hence, higher quartile is 26

Minimum is the smallest value of dataset.

Hence, minimum= 2.

Maximum is the largest value of the dataset.

Hence, maximum= 32.

The five number summary is,

2, 17, 23.5, 26, 32