Chapter 10.3, Problem 1GP

To determine

To calculate:The mean absolute deviation of the given information and also describes its representation.

Answer to Problem 1GP

The Mean Absolute Deviation of the given set of values is $M.A.D=20$ .

It shows that the average distance between actual number of rose petals and the mean number of rose petals on different types of roses is 20 rose petals.

Explanation of Solution

Given information:The table below shows the number of petals on different types of roses.

No. of Rose petals
16
17
20
22
26
33
35
35
44
52

Formula used:

The Mean of a given set of values is the average of the given set of values.

  $Mean=\frac{\text{sum}\text{of}\text{values}}{\text{number}\text{of}\text{values}}=\frac{{\displaystyle \sum x}}{n}$

The Mean Absolute Deviation of a given set of values is the average of deviation of each value from the mean value.

  $M.A.D=\frac{{\displaystyle \sum \left(|x-\overline{x}|\right)}}{n}$

Calculation:

The value of $x,\overline{x},\left(|x-\overline{x}|\right),\text{mean}\text{absolute}\text{deviation}\left(M.A.D\right)$ are shown below

$x$	$\left(|x-\overline{x}|\right)$
16	$\left(16-10\right)=6$
17	$\left(17-10\right)=7$
20	$\left(20-10\right)=10$
22	$\left(22-10\right)=12$
26	$\left(26-10\right)=16$
33	$\left(33-10\right)=23$
35	$\left(35-10\right)=25$
35	$\left(35-10\right)=25$
44	$\left(44-10\right)=34$
52	$\left(52-10\right)=42$
${\displaystyle \sum x}=300$	${\displaystyle \sum \left(|x-\overline{x}|\right)}=200$
$\overline{x}=\frac{{\displaystyle \sum x}}{n}=\frac{300}{10}=30$	$M.A.D=\frac{{\displaystyle \sum \left(|x-\overline{x}|\right)}}{n}=\frac{200}{10}=20$

The Mean Absolute Deviation of the given set of values is $M.A.D=20$ .

It shows that the average distance between actual number of rose petals and the mean number of rose petals on different types of roses is 20 rose petals.