Chapter 10, Problem 25SGR

a.

To determine

To graph a histogram for the two set of group.

Explanation of Solution

Given information:

Data of disciplinary actions taken by Ms. M and Ms. A is,

Ms. M	Ms. A
9, 16, 12, 11, 12, 9, 10, 14, 13, 10, 9, 10, 11, 9, 12, 10, 11, 12	7, 1, 0, 4, 2, 1, 6, 2, 2, 1, 4, 3, 0, 7, 0, 2, 5, 0

Graph:

Ms. M’s graph,

   Ms. A’s graph

  

b.

To determine

To calculate the 5-number summary of both data set.

Answer to Problem 25SGR

The five-number summary for Ms. M is 9, 10,11,12,16

The five-number summary for Ms. A is 0, 1,2,3,7

Explanation of Solution

Given information: Data of disciplinary actions taken by Ms. M and Ms. A is,

Ms. M	Ms. A
9, 16, 12, 11, 12, 9, 10, 14, 13, 10, 9, 10, 11, 9, 12, 10, 11, 12	7, 1, 0, 4, 2, 1, 6, 2, 2, 1, 4, 3, 0, 7, 0, 2, 5, 0

Formula used:

Minimum is, $\min =smallestValue$

Maximum is, $\max =biggestValue$

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

Lower quartile is, $q1=\frac{1}{4}(n+1)$

Upper quartile is, $q3=\frac{3}{4}(n+1)$

Calculation:

For Ms. M,

Re-arranging the data in ascending order,

9,9,9,9,10,10,10,10,11,11,11,12,12,12,12,13,14,16

For minimum, substituting the values,

  $\min =9$

Hence, minimum is 9

For maximum, substituting the values,

  $\max =16$

Hence, maximum is 16

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,

  $M=\frac{11+11}{2}$

On solving,

  $M=11$

Hence, median is 11.

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,

  $q1=10$

Hence, lower quartile is 10.

For upper quartile, substituting the values,

  $q3=\frac{3}{4}(18+1)$

On solving,

  $q3=14.25$

Rounding off,

  $\approx 14$

Substituting the value,

  $q3=12$

Hence, upper quartile is 12.

Hence, the five-number summary for Ms. M is 9, 10,11,12,16

For Ms. A,

Re-arranging the data in ascending order,

0,0,0,0,1,1,1,2,2,2,2,3,4,4,5,6,7,7

For minimum, substituting the values,

  $\min =0$

Hence, minimum is 0

For maximum, substituting the values,

  $\max =7$

Hence, maximum is 7

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,

  $M=\frac{2+2}{2}$

On solving,

  $M=2$

Hence, median is 2.

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,

  $q1=1$

Hence, lower quartile is 1.

For upper quartile, substituting the values,

  $q3=\frac{3}{4}(18+1)$

On solving,

  $q3=14.25$

Rounding off,

  $\approx 14$

Substituting the value,

  $q3=3$

Hence, upper quartile is 3.

Hence, the five-number summary for Ms. Anderson is 0, 1,2,3,7

From comparing the five number summary of Ms. M and A,

MS. M takes more disciplinary actions.