Chapter 4, Problem 1.1Q

Summary Introduction

Interpretation: The mean error of the HR department’s forecast is to be determined along with mean absolute deviation and mean absolute percent error.

Concept Introduction: The following formula will be used:

  $Meanabsolutedeviation=\frac{error}{totalnumber}$

  $mean=\frac{Totalofactualattendance}{Totalsession}$

  $Meanabsoluteerror=\frac{error}{actualvalue}\times 100$

Answer to Problem 1.1Q

Mean error = 0.81530

Mean absolute deviation = 1.7

Mean absolute percent error = 21.88%

Explanation of Solution

The following formula will be used to calculate the mean for HR department’s forecast −

  $=\frac{Totalofactualattendance}{Totalsession}$

Actual attendance = 95

Total session = 10

Therefore,

  $=\frac{\text{95 }}{10}=9.5$

The difference between actual attendance and mean attendance results the deviation from actual value.

${\left(Actualattendance–meanattendance\right)}^2$
${\left(13-9.5\right)}^2$	12.25
${\left(10-9.5\right)}^2$	0.25
${\left(12-9.5\right)}^2$	6.25
${\left(12-9.5\right)}^2$	6.25
${\left(8-9.5\right)}^2$	2.25
${\left(11-9.5\right)}^2$	2.25
${\left(9-9.5\right)}^2$	0.25
${\left(9-9.5\right)}^2$	0.25
${\left(4-9.5\right)}^2$	30.25
${\left(7-9.5\right)}^2$	6.25
Summation	66.5

The standard deviation can be calculated as −

  $S.D.=\sqrt{\frac{66.5}{10}}=2.578$

The following method will be used to calculate the standard error −

  $S.E.=\frac{S.D.}{\sqrt{10}}=\frac{2.578}{3.162}=0.81530$

Mean absolute deviation can be calculated as −

$\left(Actualattendance–forecastattendance\right)$	error
$\left(13-10\right)$	3
$\left(10-10\right)$	0
$\left(12-10\right)$	2
$\left(12-10\right)$	2
$\left(8-10\right)$	-2
$\left(11-10\right)$	1
$\left(9-10\right)$	-1
$\left(9-10\right)$	-1
$\left(4-10\right)$	-6
$\left(7-10\right)$	-3
Summation	17

  $Meanabsolutedeviation=\frac{error}{totalnumber}$

  $=\frac{17}{10}=1.7$

The following formula will be used to calculate the mean absolute error for each component −

  $Meanabsoluteerror=\frac{error}{actualvalue}\times 100$

Therefore,

Actual attendance	error	$\frac{error}{actualvalue}\times 100$
13	3	$\frac{3}{13}\times 100=23.07\%$
10	0	$\frac{0}{10}\times 100=0\%$
12	2	$\frac{2}{12}\times 100=16.66\%$
12	2	$\frac{2}{12}\times 100=16.66\%$
8	-2	$\frac{-2}{8}\times 100=-8.33$
11	1	$\frac{1}{11}\times 100=9.09\%$
9	-1	$\frac{-1}{9}\times 100=-11.11\%$
9	-1	$\frac{-1}{9}\times 100=-11.11\%$
4	-6	$\frac{-6}{4}\times 100=-150\%$
7	-3	$\frac{-3}{7}\times 100=-42.85\%$
	Summation	$\frac{216.88}{10}=21.88\%$