Sheepdog SprocketData & Chance · statistics and probability

Measures how far each sheep strays from the middle: mean absolute deviation and standard deviation.

Spread About the Mean

Mean absolute deviation and standard deviation. In MathBound, the free Algebra I adventure game, Sheepdog Sprocket asks these problems, and the only way past is to solve them.

Part of Data Analysis: chapter 12 of the standard course.

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What you will practice

Mean Absolute Deviation and Standard Deviation. Find deviations from the mean and the mean absolute deviation of a small data set.

Worked examples

Made by the game’s own question engine. Try each one, then open its steps.

Example 1 · Mean Absolute Deviation and Standard Deviation

The

mean

of

38, 24, 29, 23, 6

is

24 .

What

is

the

deviation

of

23

from

the

mean?

$24$
$1$
$23$
$- 1$

Show the worked steps

$A$ $deviation$ $is$ $the$ $value$ $minus$ $the$ $mean.$
$23 - 24 = - 1.$

Answer: $- 1$

Example 2 · Mean Absolute Deviation and Standard Deviation

The

deviations

from

the

mean

of

a

data

set

of

6

values

are

6, - 2, - 4, 1, - 2

and

one

more.

What

is

the

missing

deviation?

$- 1$
$1$
$0$
$15$

Show the worked steps

$The$ $deviations$ $from$ $the$ $mean$ $always$ $add$ $up$ $to$ $0.$
$The$ $given$ $ones$ $add$ $up$ $to$ $- 1,$ $so$ $the$ $missing$ $one$ $is$ $1.$

Answer: $1$

Example 3 · Mean Absolute Deviation and Standard Deviation

Over

a

season,

the

Hawks

scored

a

mean

of

65

points

a

game

with

standard

deviation

6;

the

Owls

scored

a

mean

of

67

points

with

standard

deviation

2 .

Which

statement

is

true?

$The$ $Owls$ $scored$ $more$ $on$ $average,$ $and$ $the$ $Owls$ $were$ $more$ $consistent$
$The$ $Hawks$ $scored$ $more$ $on$ $average,$ $and$ $the$ $Owls$ $were$ $more$ $consistent$
$The$ $Owls$ $scored$ $more$ $on$ $average,$ $and$ $the$ $Hawks$ $were$ $more$ $consistent$
$The$ $Hawks$ $scored$ $more$ $on$ $average,$ $and$ $the$ $Hawks$ $were$ $more$ $consistent$

Show the worked steps

$The$ $higher$ $mean,$ $67,$ $belongs$ $to$ $the$ $Owls.$
$The$ $smaller$ $standard$ $deviation,$ $2,$ $means$ $less$ $spread:$ $the$ $Owls$ $were$ $more$ $consistent.$

Answer: $The$ $Owls$ $scored$ $more$ $on$ $average,$ $and$ $the$ $Owls$ $were$ $more$ $consistent$

Where it is in your textbook

Textbook	Lessons
Standard course	12.2
Big Ideas Math Algebra 1	11.1
Big Ideas Math Algebra 1 (2022)	11.1
Carnegie Learning Algebra I	M4 1.2, M4 1.3
CPM Core Connections Algebra	11.2.3
CPS Skyline Algebra	9.1-9.2
enVision Algebra 1	11-4
enVision Algebra 1 (2024)	11-4
Eureka Math Algebra I (EngageNY)	2.4-2.6
Glencoe Algebra 1	12-2, 12-4
HMH Into Algebra 1	22.1
Holt McDougal Larson Algebra 1	10.2
Illustrative Mathematics Algebra 1	1.4-1.5, 1.12-1.13, 1.14, 1.15-1.16
Illustrative Mathematics Algebra 1 (v.360)	1.4-1.5, 1.12-1.13, 1.14, 1.15-1.16
MVP Mathematics I (Integrated Math 1)	9.7, 9.8
Open Up NC Math 1 (MVP)	9.7, 9.8
Pearson Algebra 1 Common Core	12-3
Reveal Algebra 1	12-4, 12-6
SpringBoard Algebra 1	36

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