Learning Dot Plots and Mean Absolute Deviation
Lesson
Dot Plots and Measure of
Variation with Mean
Absolute Deviation
[
OBJECTIVE
]
•
The student will use dot plots and data sets to
determine mean absolute deviation.
[
MY
SKILLS
]
•
Dot plots
•
Variability
•
Absolute Value
•
Mean
•
Median
•
Center
[
ESSENTIAL
QUESTIONS
]
1.
What is the MAD (mean absolute deviation)?
2.
How can I use the mean to help determine
the MAD of a set of data?
3.
What characteristics of a data set impact the
MAD?
[Warm-Up]
Begin by completing the warm-up for this lesson
MEASURE OF CENTER - MEAN
SOLVE Problem
SOLVE
Mr. Tomas is working with his math class on
collecting data. He asks students to measure the
arm span of their partner and record it in their
math notebook for the project. The arm spans of
seven of the students are listed below. What is
the mean arm span length?
Arm span of seven students in inches:
60, 54, 48, 51, 59, 57, 56
S
Study the Problem
Underline the question.
This problem is asking me to find
the mean of the length of the arm spans.
SOLVE
Mr. Tomas is working with his math class on
collecting data. He asks students to measure the
arm span of their partner and record it in their
math notebook for the project. The arm spans of
seven of the students are listed below. What is
the mean arm span length?
Arm span of seven students in inches:
60, 54, 48, 51, 59, 57, 56
O
Organize the Facts
Identify the facts.
Eliminate the unnecessary facts.
List the necessary facts.
•
A
r
m
s
p
a
n
s
i
n
i
n
c
h
e
s
:
6
0
,
5
4
,
4
8
,
5
1
,
5
9
,
5
7
,
5
6
L
Line Up a Plan
Write in words what your plan of action will
be.
Find the sum of the arm spans and then
divide by the number of data values.
Choose an operation or operations.
Addition, Division
V
Verify Your Plan with Action
Estimate your answer.
About 50 inches
Carry out your plan.
60 + 54 + 48 + 51 + 59 + 57 + 56 = 385
385 ÷ 7 = 55 inches
E
Examine Your Results
Does your answer make sense?
(compare your answer to question.)
Yes, because I was looking for the mean of
the measure of the arm span of the students.
Is your answer reasonable?
(compare your answer to the estimate.)
Yes, because it is close to my estimate of
about 50 inches.
Is your answer accurate?
(check your work.)
Yes.
Write your answer in a complete sentence.
The length of the mean arm span is 55
inches.
EXTEND THE SOLVE PROBLEM –
DETERMINING THE DEVIATION FROM
THE MEAN
Discovery Activity
Discovery Activity – Extend the SOLVE
Problem – Determining the Deviation
from the Mean
What type of measure were we finding
when we found the
mean
in the SOLVE
problem?
measure of center
Discovery Activity – Extend the SOLVE
Problem – Determining the Deviation
from the Mean
What is a “measure of center?”
A measure of center is numerical data
described in a single value.
Can you name another measure of
center that we use?
Median
Discovery Activity – Extend the SOLVE
Problem – Determining the Deviation
from the Mean
When working with box plots we found
the IQR. What is the IQR a measure of?
Variability
What does the IQR describe?
It describes the variability in the
middle 50% of the data.
Discovery Activity – Extend the SOLVE
Problem – Determining the Deviation
from the Mean
What is “measure of variability?”
Measure of variability describes how
the values vary when compared to a
single number.
With your partner, discuss ways that
you can use the mean.
Discovery Activity – Extend the SOLVE
Problem – Determining the Deviation
from the Mean
What type of graph is shown?
A number line
Discovery Activity – Extend the SOLVE
Problem – Determining the Deviation
from the Mean
What is the lowest value on the number line?
48
What is the greatest value on the number line?
60
Discovery Activity – Extend the SOLVE
Problem – Determining the Deviation
from the Mean
Place a dot to represent each data value from the
SOLVE problem.
What is the mean of the
data set
?
55
Mark the mean on the number line
with a star.
Discovery Activity – Extend the SOLVE
Problem – Determining the Deviation
from the Mean
Let’s start by listing all of the data
values marked on the number line.
48
51
54
56
57
59
60
Discovery Activity – Extend the SOLVE
Problem – Determining the Deviation
from the Mean
Identify the placement of the lowest
value on the number line.
48
Discuss ways that you can determine
the distance from the mean of 55 to
the lowest value of 48 using the
number line.
Discovery Activity – Extend the SOLVE
Problem – Determining the Deviation
from the Mean
How can we find the distance from the mean to
the least value, using the number line?
Since the values in the number line use a
scale of 1, we can start at 55 and mark each
space moved until we reach 48.
Discovery Activity – Extend the SOLVE
Problem – Determining the Deviation
from the Mean
How many spaces do we need to move?
7
Discovery Activity – Extend the SOLVE
Problem – Determining the Deviation
from the Mean
Did we move to the right or the left on
the number line?
48
51
54
56
57
59
60
7
Left
Discovery Activity – Extend the SOLVE
Problem – Determining the Deviation
from the Mean
What does it mean when we move to the left on
the number line?
It is a move in the negative direction.
Discovery Activity – Extend the SOLVE
Problem – Determining the Deviation
from the Mean
We moved to the left, therefore, this
was a negative move.
48
51
54
56
57
59
60
7
Left
Negative
Discovery Activity – Extend the SOLVE
Problem – Determining the Deviation
from the Mean
How can we model that move using an
integer?
48
51
54
56
57
59
60
7
Left
Negative
-
7
Discovery Activity – Extend the SOLVE
Problem – Determining the Deviation
from the Mean
This is called the deviation from the mean.
48
51
54
56
57
59
60
7
Left
Negative
-
7
Discovery Activity – Extend the SOLVE
Problem – Determining the Deviation
from the Mean
What is “Deviation from the Mean?”
Deviation is how the data value is different
from the mean.
Can a distance ever be a negative number?
No.
For example, you cannot walk a negative 7 steps.
Discovery Activity – Extend the SOLVE
Problem – Determining the Deviation
from the Mean
What is “Absolute Value?”
The distance a number is from zero on a
number line.
What do you think that means for
absolute deviation?
Absolute deviation must be a positive value.
Discovery Activity – Extend the SOLVE
Problem – Determining the Deviation
from the Mean
What is the absolute deviation for 48?
7
Discovery Activity – Extend the SOLVE
Problem – Determining the Deviation
from the Mean
The absolute deviation of 48 is 7.
48
51
54
56
57
59
60
7
Left
Negative
-
7
7
Discovery Activity – Extend the SOLVE
Problem – Determining the Deviation
from the Mean
Since the values in the number line use a
scale of 1, we can start at 55 and mark each
space moved until we reach 51.
What is the next value on the number line?
51
How can we find the distance from the mean to 51?
Discovery Activity – Extend the SOLVE
Problem – Determining the Deviation
from the Mean
How many spaces do we need to move?
4
Did we move to the right or to the left?
We moved to the left which means it
was a negative move.
Discovery Activity – Extend the SOLVE
Problem – Determining the Deviation
from the Mean
Move 4 inches to left (negative).
48
51
54
56
57
59
60
7
Left
Negative
-
7
7
4
Left
Negative
Discovery Activity – Extend the SOLVE
Problem – Determining the Deviation
from the Mean
What is the deviation from the mean?
–
4
Can a distance ever be a negative number?
No. You cannot walk a negative 4 steps.
Discovery Activity – Extend the SOLVE
Problem – Determining the Deviation
from the Mean
What do you think that means for the
absolute deviation?
It must be a positive value.
What is the absolute deviation for 51?
4
Discovery Activity – Extend the SOLVE
Problem – Determining the Deviation
from the Mean
Complete the graphic organizer.
48
51
54
56
57
59
60
7
Left
Negative
-
7
7
4
Left
Negative
-
4
4
Discovery Activity – Extend the SOLVE
Problem – Determining the Deviation
from the Mean
48
51
54
56
57
59
60
7
Left
Negative
-
7
7
4
Left
Negative
-
4
4
1
Left
Negative
-
1
1
1
Right
Positive
1
1
2
Right
Positive
2
2
4
Right
Positive
4
4
5
Right
Positive
5
5
EXTEND THE SOLVE PROBLEM –
DETERMINING THE MEAN ABSOLUTE
DEVIATION
Discovery Activity
Discovery Activity – Extend the SOLVE
Problem – Determining the Mean
Absolute Deviation
What is the total of the absolute deviation
values?
Add all seven numbers:
7 + 4 + 1 + 1 + 2 + 4 + 5 = 24
How do we determine the mean of the
absolute deviation values?
Find the sum and divide by the number of values.
24 ÷ 7 = 3.43 rounded to the nearest hundredth
Discovery Activity – Extend the SOLVE
Problem – Determining the Mean
Absolute Deviation
48
51
54
56
57
59
60
7
Left
Negative
4
Left
Negative
1
Left
Negative
1
Right
Positive
2
Right
Positive
4
Right
Positive
5
Right
Positive
24
3.43
-
7
7
-
4
4
-
1
1
1
1
2
2
4
4
5
5
Discovery Activity – Extend the SOLVE
Problem – Determining the Mean
Absolute Deviation
The MAD (mean absolute deviation) for the
data set is 3.43. This means that on average, the
arm span of the students varies 3.43 inches
from the mean of 55 inches.
Discovery Activity – Extend the SOLVE
Problem – Determining the Mean
Absolute Deviation
What does the mean show us?
The mean gives the measure of center
of the data set with a single number.
What does the MAD show us?
The mean absolute deviation describes how
the data values vary from the mean with a
single number.
DETERMINING THE MEAN
ABSOLUTE DEVIATION
SOLVE
SOLVE
During the math unit on measurement, Mr. Tomas also
had students collect information about foot length. The
foot lengths of the eight students are listed below. Foot
length of eight students in inches:
What are the mean and the MAD of the data set for
the foot length of the eight students? Explain what
each value means for the data set.
S
Study the Problem
Underline the question.
This problem is asking me to find
the mean and MAD of the foot lengths of the eight
students and explain what each term means for the
data set.
During the math unit on measurement, Mr.
Tomas also had students collect information
about foot length. The foot lengths of the eight
students are listed below. Foot length of eight
students in inches:
What are the mean and the MAD of the data set
for the foot length of the eight students? Explain
what each value means for the data set.
O
Organize the Facts
Identify the facts.
Eliminate the unnecessary facts.
List the necessary facts.
Foot length of eight students in inches:
L
Line Up a Plan
Write in words what your plan of action will
be.
Mean: Find the sum of the values and then
divide by the number of values to determine
the mean.
Choose an operation or operations.
Mean: addition, division
L
Line Up a Plan
Write in words what your plan of action will be.
MAD: Put the scores in order from least to
greatest. Place the values on a number line.
Mark the mean on the number line. Count the
number of spaces from each value to the mean
and chart the absolute deviation for each. Find
the total of the values for absolute deviation
and divide by the number of values in that
column to determine the MAD.
Choose an operation or operations.
MAD: addition, division
V
Verify
Your Plan with Action
Estimate your answer.
mean: about 12
MAD: about 2
Carry out your plan.
V
Verify
Your Plan with Action
Estimate your answer.
mean: about 12
MAD: about 2
Carry out your plan.
Values in order:
V
Verify Your Plan with Action
Carry out your plan.
11
2 in.
Left
Negative
-
2
2
Left
Negative
1 in.
Left
Negative
-
1
7
Left
Negative
Right
Positive
1 in.
Right
Positive
1
1
Right
Positive
10
1.25 in.
12
14
15
2 in.
Right
Positive
2
2
E
Examine Your Results
Does your answer make sense?
(compare your answer to question.)
Yes, because I was looking for the mean and
MAD of the foot lengths.
Is your answer reasonable?
(compare your answer to the estimate.)
Yes, because it is close to my estimate of
about 12 for the mean and about 2 for the
MAD.
Is your answer accurate?
(check your work.)
Yes.
Write your answer in a complete sentence.
The mean foot length is 13 inches. This
means the average foot length of the eight
students is 13 inches. The MAD of the data
set is 1.25 inches. This means that on
average, the foot length of any student varies
1.25 inches from the mean of 13 inches.
USING A DOT PLOT TO DETERMINE
MEAN ABSOLUTE DEVIATION - MAD
Using a Dot Plot to Determine Mean
Absolute Deviation
3. The following dot plot shows the distance
from home to school in miles of a group of
students.
Why do we need to find the mean before the MAD?
We need to know the mean in order to determine
how the other values deviate from the mean.
Distance to School from Home in Miles
Using a Dot Plot to Determine Mean
Absolute Deviation
How is this example different?
The data is given in a dot plot instead of a list.
With your partner, find the mean.
1 + 2 + 4 + 5 + 6 + 7 + 9 + 10 = 44
44 ÷ 8 = 5.5 miles
Distance to School from Home in Miles
Using a Dot Plot to Determine Mean
Absolute Deviation
What is the lowest value on the number line?
1
Discuss possible strategies to determine the
distance from the mean of 5.5 to the lowest
value of 1 without drawing the moves on the
number line.
Distance to School from Home in Miles
Using a Dot Plot to Determine Mean
Absolute Deviation
How can we find the distance from the mean to
the lowest value, without using the number
line?
Find the difference of the two values
Distance to School from Home in Miles
Using a Dot Plot to Determine Mean
Absolute Deviation
What is the difference of the two values?
4.5
Distance to School from Home in Miles
Using a Dot Plot to Determine Mean
Absolute Deviation
What does it mean when the value is to the left
of the mean on the number line?
The deviation is in the negative direction so it will
be a negative value.
Distance to School from Home in Miles
Using a Dot Plot to Determine Mean
Absolute Deviation
What is the deviation from the mean?
–
4.5
Distance to School from Home in Miles
What is the absolute deviation?
4.5
Using a Dot Plot to Determine Mean
Absolute Deviation
1
2
4
5
6
7
9
Negative
-
4.5
4.5
10
4.5
Using a Dot Plot to Determine Mean
Absolute Deviation
What is the next value on the number line?
2
Discuss possible strategies to determine the
distance from the mean of 5.5 to the value of 2
without drawing the moves on the number line.
Distance to School from Home in Miles
Using a Dot Plot to Determine Mean
Absolute Deviation
How can we find the distance from the mean to
the value of 2, without using the number line?
Find the difference of the two values.
Distance to School from Home in Miles
Using a Dot Plot to Determine Mean
Absolute Deviation
What is the difference of the two values?
3.5
Distance to School from Home in Miles
Using a Dot Plot to Determine Mean
Absolute Deviation
What does it mean when the value is to the left
of the mean on the number line?
The deviation is in the negative direction, so it will
be a negative value.
Distance to School from Home in Miles
Using a Dot Plot to Determine Mean
Absolute Deviation
What is the deviation from the mean?
–
3.5
Distance to School from Home in Miles
What is the absolute deviation?
3.5
Using a Dot Plot to Determine Mean
Absolute Deviation
1
2
4
5
6
7
9
Negative
-
4.5
4.5
10
4.5
Negative
-
3.5
3.5
3.5
Using a Dot Plot to Determine Mean
Absolute Deviation
Complete the rest of the graphic organizer.
Distance to School from Home in Miles
Using a Dot Plot to Determine Mean
Absolute Deviation
1
2
4
5
6
7
9
Negative
-
4.5
4.5
10
4.5
Negative
-
3.5
3.5
3.5
Negative
-
1.5
1.5
1.5
Negative
-
3.5
3.5
0.5
Positive
0.5
0.5
0.5
Positive
0.5
0.5
1.5
Positive
3.5
3.5
3.5
Positive
4.5
4.5
4.5
Using a Dot Plot to Determine Mean
Absolute Deviation
How do we determine the total?
Distance to School from Home in Miles
Add the sum of all the values in the absolute
deviation column.
Using a Dot Plot to Determine Mean
Absolute Deviation
What is the total?
20.0
Distance to School from Home in Miles
How do we determine the MAD?
By dividing the total by the number of data values
we added.
Using a Dot Plot to Determine Mean
Absolute Deviation
Explain how you found the MAD
Distance to School from Home in Miles
Divide 20.0 by 8 for a quotient of 2.50 miles.
Using a Dot Plot to Determine Mean
Absolute Deviation
1
2
4
5
6
7
9
Negative
-
4.5
4.5
10
4.5
Negative
-
3.5
3.5
3.5
Negative
-
1.5
1.5
1.5
Negative
-
3.5
3.5
0.5
Positive
0.5
0.5
0.5
Positive
0.5
0.5
1.5
Positive
3.5
3.5
3.5
Positive
4.5
4.5
4.5
20.0
2.50 miles
Using a Dot Plot to Determine Mean
Absolute Deviation
What does the mean represent?
The average distance from home to school of the
eight students
What does the MAD (mean absolute deviation)
represent?
The amount that each of the eight students’
distances vary from the mean of 5.5 miles.
WORKING WITH MEAN ABSOLUTE
DEVIATION - MAD
Working with Mean Absolute
Deviation - MAD
Take a look at the graphic organizer
on the top of the next page.
It contains the information for Problems 1-3
that we have completed in the lesson.
Working with Mean Absolute
Deviation - MAD
What is the range of values for Problem 1?
12
Working with Mean Absolute
Deviation - MAD
What is the mean for Problem 1?
12
55
Working with Mean Absolute
Deviation - MAD
What is the MAD for Problem 1?
12
55
3.43
Working with Mean Absolute
Deviation - MAD
Identify the range, mean and MAD for
Problems 2 and 3.
12
55
3.43
4
13
1.25
9
5.5
2.5
Using a Dot Plot to Determine Mean
Absolute Deviation
Can you see any patterns?
The larger the range, the higher the MAD.
Why might that be true?
The larger the range of values, the bigger the
difference between each value and the mean,
which in turn would create a larger MAD.
Working with Mean Absolute
Deviation - MAD
In conclusion: Higher values represent a greater
variability in the data.
12
55
3.43
4
13
1.25
9
5.5
2.5
Higher values represent a greater variability in the data.
Working with Mean Absolute
Deviation - MAD
Let’s add our information from
Problem 4 to the table.
12
55
3.43
4
13
1.25
9
5.5
2.5
Higher values represent a greater variability in the data.
9
6
1.53
Working with Mean Absolute
Deviation - MAD
After adding our information from Problem 4 to our
table at the top of the page, what do you notice?
Problems 3 and 4 both had a range of 9, but the
MAD was different for the two problems.
Working with Mean Absolute
Deviation - MAD
Take a look at the data chart from Problem 3. What
do you notice about the values for Problem 3?
None of them are duplicated
What do you notice about the data values for
Problem 4?
There are multiple values of 4, 5, 6 and 7.
Working with Mean Absolute
Deviation - MAD
What conclusion can you make about the effect
repeated values have on the MAD?
There was a greater number of data values, and
many of them were clustered near the mean.
MEAN ABSOLUTE DEVIATION - MAD
SOLVE
SOLVE
A group of teachers at Capital Junior High are
walking each week for a health challenge. The
teachers chart the number of miles they each
walk during the week. The data from last week’s
walking totals are shown below. What is the
mean number of miles walked last week and the
MAD for the data set?
Number of Miles Walked in a Week:
9, 12, 13, 15, 2, 19, 9, 8, 13, 14, 17, 10, 13, 14
S
Study the Problem
Underline the question.
This problem is asking me to find
the mean of the data set and the MAD.
SOLVE
A group of teachers at Capital Junior High are
walking each week for a health challenge. The
teachers chart the number of miles they each
walk during the week. The data from last week’s
walking totals are shown below. What is the
mean number of miles walked last week and the
MAD for the data set?
Number of Miles Walked in a Week:
9, 12, 13, 15, 2, 19, 9, 8, 13, 14, 17, 10, 13, 14
O
Organize the Facts
Identify the facts.
Eliminate the unnecessary facts.
List the necessary facts.
M
i
l
e
s
:
9
,
1
2
,
1
3
,
1
5
,
2
,
1
9
,
9
,
8
,
1
3
,
1
4
,
1
7
,
1
0
,
1
3
,
1
4
L
Line Up a Plan
Write in words what your plan of action will
be.
Find the mean of the data set by adding the
values and dividing by the number of values.
Find the MAD by determining the absolute
deviation of each data value and then adding
and dividing to determine the MAD.
Choose an operation or operations.
Addition, Division
V
Verify Your Plan with Action
Estimate your answer.
Mean: About 10 miles, MAD: about 2.5 miles
Carry out your plan.
Mean:
9 + 12 + 13 + 15 + 2 + 17 + 9 + 8 + 13 + 14 + 19
+ 10 + 13 + 14 = 168
168 ÷ 14 = 12 miles
V
Verify Your Plan with Action
Carry out your plan.
MAD
V
Verify Your Plan with Action
Carry out your plan.
MAD
Total of absolute deviation values = 44
MAD (mean absolute deviation)
= 44 ÷ 14 = 3.14
E
Examine Your Results
Does your answer make sense?
(compare your answer to question.)
Yes, because I was looking for the mean and
MAD of the miles walked.
Is your answer reasonable?
(compare your answer to the estimate.)
Yes, because it is close to my estimate of
about 10 miles for the mean and about 2.5
miles for the MAD.
Is your answer accurate?
(check your work.)
Yes.
Write your answer in a complete sentence.
The mean of the miles walked is 12 miles.
This means the average of the miles walked
for the 14 teachers is 12 miles. The MAD of
the data set is 3.14 miles. This means that on
average, the miles walked by any teacher
varies 3.14 miles from the mean of 12 miles.
DOT PLOTS AND MEASURE OF
VARIATION WITH MEAN ABSOLUTE
DEVIATION
Closure
[
ESSENTIAL
QUESTIONS
]
1.
What is the MAD (mean absolute deviation)?
The mean absolute deviation is a measure of
variability of a data set. It is represented by a
single value and the higher the value, the
greater the variability in the data.
2.
How can I use the mean to help determine the
MAD of a set of data?
When determining the MAD – mean absolute
deviation – you must determine the deviation
of each data value from the mean.
[
ESSENTIAL
QUESTIONS
]
3.
What characteristics of a data set impact the
MAD?
Possible answers include: duplicate data
values can signify a cluster, if there are more
data values, then the MAD may be affected.
Mean
Measure of Center
Median
IQR (interquartile range)
Measure of Variability
Data set
Deviation from the Mean
Absolute value
Absolute deviation
MAD (mean absolute deviation)
Lesson
Dot Plots and Measure of
Variation with Mean
Absolute Deviation
In this lesson, students will explore dot plots and measure variation with mean absolute deviation. They will learn to calculate the mean arm span length using a set of data and understand the characteristics impacting the mean absolute deviation. Essential questions guide the learning process, reinforcing understanding of the MAD concept. Practical problems like determining the mean arm span from student measurements engage students in applying mathematical concepts to real-world scenarios. Through warm-up activities and problem-solving tasks, students enhance their skills in interpreting data and deriving meaningful insights.
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Presentation Transcript
Lesson Dot Plots and Measure of Variation with Mean Absolute Deviation
[OBJECTIVE] The student will use dot plots and data sets to determine mean absolute deviation.
[MYSKILLS] Dot plots Variability Absolute Value Mean Median Center
[ESSENTIALQUESTIONS] 1. What is the MAD (mean absolute deviation)? 2. How can I use the mean to help determine the MAD of a set of data? 3. What characteristics of a data set impact the MAD?
[Warm-Up] Begin by completing the warm-up for this lesson
SOLVE Problem MEASURE OF CENTER - MEAN
SOLVE Mr. Tomas is working with his math class on collecting data. He asks students to measure the arm span of their partner and record it in their math notebook for the project. The arm spans of seven of the students are listed below. What is the mean arm span length? Arm span of seven students in inches: 60, 54, 48, 51, 59, 57, 56 S Study the Problem Underline the question. This problem is asking me to find the mean of the length of the arm spans.
SOLVE Mr. Tomas is working with his math class on collecting data. He asks students to measure the arm span of their partner and record it in their math notebook for the project. The arm spans of seven of the students are listed below. What is the mean arm span length? Arm span of seven students in inches: 60, 54, 48, 51, 59, 57, 56 O Organize the Facts Identify the facts. Eliminate the unnecessary facts. List the necessary facts. Arm spans in inches: 60, 54, 48, 51, 59, 57, 56
L Line Up a Plan Write in words what your plan of action will be. Find the sum of the arm spans and then divide by the number of data values. Choose an operation or operations. Addition, Division
V Verify Your Plan with Action Estimate your answer. About 50 inches Carry out your plan. 60 + 54 + 48 + 51 + 59 + 57 + 56 = 385 385 7 = 55 inches
E Examine Your Results Does your answer make sense? (compare your answer to question.) Yes, because I was looking for the mean of the measure of the arm span of the students. Is your answer reasonable? (compare your answer to the estimate.) Yes, because it is close to my estimate of about 50 inches.
Is your answer accurate? (check your work.) Yes. Write your answer in a complete sentence. The length of the mean arm span is 55 inches.
Discovery Activity EXTEND THE SOLVE PROBLEM DETERMINING THE DEVIATION FROM THE MEAN
Discovery Activity Extend the SOLVE Problem Determining the Deviation from the Mean What type of measure were we finding when we found the mean in the SOLVE problem? measure of center
Discovery Activity Extend the SOLVE Problem Determining the Deviation from the Mean What is a measure of center? A measure of center is numerical data described in a single value. Can you name another measure of center that we use? Median
Discovery Activity Extend the SOLVE Problem Determining the Deviation from the Mean When working with box plots we found the IQR. What is the IQR a measure of? Variability What does the IQR describe? It describes the variability in the middle 50% of the data.
Discovery Activity Extend the SOLVE Problem Determining the Deviation from the Mean What is measure of variability? Measure of variability describes how the values vary when compared to a single number. With your partner, discuss ways that you can use the mean.
Discovery Activity Extend the SOLVE Problem Determining the Deviation from the Mean 49 50 51 52 53 54 55 56 57 58 60 48 59 What type of graph is shown? A number line
Discovery Activity Extend the SOLVE Problem Determining the Deviation from the Mean 49 50 51 52 53 54 55 56 57 58 60 48 59 What is the lowest value on the number line? 48 What is the greatest value on the number line? 60
Discovery Activity Extend the SOLVE Problem Determining the Deviation from the Mean 49 50 51 52 53 54 55 56 57 58 60 48 59 Place a dot to represent each data value from the SOLVE problem. What is the mean of the data set? 55 Mark the mean on the number line with a star.
Discovery Activity Extend the SOLVE Problem Determining the Deviation from the Mean Data Value Number of inches from Mean Left or Right Positive or negative Deviation from Mean Absolute Deviation 48 51 54 56 57 59 60 Let s start by listing all of the data values marked on the number line.
Discovery Activity Extend the SOLVE Problem Determining the Deviation from the Mean Identify the placement of the lowest value on the number line. 48 Discuss ways that you can determine the distance from the mean of 55 to the lowest value of 48 using the number line.
Discovery Activity Extend the SOLVE Problem Determining the Deviation from the Mean 49 50 51 52 53 54 55 56 57 58 60 48 59 How can we find the distance from the mean to the least value, using the number line? Since the values in the number line use a scale of 1, we can start at 55 and mark each space moved until we reach 48.
Discovery Activity Extend the SOLVE Problem Determining the Deviation from the Mean 49 50 51 52 53 54 55 56 57 58 60 48 59 How many spaces do we need to move? 7
Discovery Activity Extend the SOLVE Problem Determining the Deviation from the Mean Data Value Number of inches from Mean Left or Right Positive or negative Deviation from Mean Absolute Deviation 7 Left 48 51 54 56 57 59 60 Did we move to the right or the left on the number line?
Discovery Activity Extend the SOLVE Problem Determining the Deviation from the Mean 49 50 51 52 53 54 55 56 57 58 60 48 59 What does it mean when we move to the left on the number line? It is a move in the negative direction.
Discovery Activity Extend the SOLVE Problem Determining the Deviation from the Mean Data Value Number of inches from Mean 7 Left or Right Positive or negative Negative Deviation from Mean Absolute Deviation Left 48 51 54 56 57 59 60 We moved to the left, therefore, this was a negative move.
Discovery Activity Extend the SOLVE Problem Determining the Deviation from the Mean Data Value Number of inches from Mean Left or Right Positive or negative Deviation from Mean Absolute Deviation -7 7 Left Negative 48 51 54 56 57 59 60 How can we model that move using an integer?
Discovery Activity Extend the SOLVE Problem Determining the Deviation from the Mean Data Value Number of inches from Mean Left or Right Positive or negative Deviation from Mean Absolute Deviation -7 7 Left Negative 48 51 54 56 57 59 60 This is called the deviation from the mean.
Discovery Activity Extend the SOLVE Problem Determining the Deviation from the Mean 49 50 51 52 53 54 55 56 57 58 60 48 59 What is Deviation from the Mean? Deviation is how the data value is different from the mean. Can a distance ever be a negative number? No. For example, you cannot walk a negative 7 steps.
Discovery Activity Extend the SOLVE Problem Determining the Deviation from the Mean 49 50 51 52 53 54 55 56 57 58 60 48 59 What is Absolute Value? The distance a number is from zero on a number line. What do you think that means for absolute deviation? Absolute deviation must be a positive value.
Discovery Activity Extend the SOLVE Problem Determining the Deviation from the Mean 49 50 51 52 53 54 55 56 57 58 60 48 59 What is the absolute deviation for 48? 7
Discovery Activity Extend the SOLVE Problem Determining the Deviation from the Mean Data Value Number of inches from Mean Left or Right Positive or negative Deviation from Mean Absolute Deviation -7 7 Left Negative 7 48 51 54 56 57 59 60 The absolute deviation of 48 is 7.
Discovery Activity Extend the SOLVE Problem Determining the Deviation from the Mean 49 50 51 52 53 54 55 56 57 58 60 48 59 What is the next value on the number line? 51 How can we find the distance from the mean to 51? Since the values in the number line use a scale of 1, we can start at 55 and mark each space moved until we reach 51.
Discovery Activity Extend the SOLVE Problem Determining the Deviation from the Mean 49 50 51 52 53 54 55 56 57 58 60 48 59 How many spaces do we need to move? 4 Did we move to the right or to the left? We moved to the left which means it was a negative move.
Discovery Activity Extend the SOLVE Problem Determining the Deviation from the Mean Data Value Number of inches from Mean Left or Right Positive or negative Deviation from Mean Absolute Deviation -7 7 4 Left Left Negative Negative 7 48 51 54 56 57 59 60 Move 4 inches to left (negative).
Discovery Activity Extend the SOLVE Problem Determining the Deviation from the Mean 49 50 51 52 53 54 55 56 57 58 60 48 59 What is the deviation from the mean? 4 Can a distance ever be a negative number? No. You cannot walk a negative 4 steps.
Discovery Activity Extend the SOLVE Problem Determining the Deviation from the Mean 49 50 51 52 53 54 55 56 57 58 60 48 59 What do you think that means for the absolute deviation? It must be a positive value. What is the absolute deviation for 51? 4
Discovery Activity Extend the SOLVE Problem Determining the Deviation from the Mean Data Value Number of inches from Mean Left or Right Positive or negative Deviation from Mean Absolute Deviation -7 -4 7 4 Left Left Negative Negative 7 4 48 51 54 56 57 59 60 Complete the graphic organizer.
Discovery Activity Extend the SOLVE Problem Determining the Deviation from the Mean Data Value Number of inches from Mean 7 4 1 1 2 4 5 Left or Right Positive or negative Negative Negative Negative Positive Positive Positive Positive Deviation from Mean Absolute Deviation -7 -4 -1 1 2 4 5 Left Left Left Right Right Right Right 7 4 1 1 2 4 5 48 51 54 56 57 59 60 Total of absolute deviation values MAD (mean absolute deviation)
Discovery Activity EXTEND THE SOLVE PROBLEM DETERMINING THE MEAN ABSOLUTE DEVIATION
Discovery Activity Extend the SOLVE Problem Determining the Mean Absolute Deviation What is the total of the absolute deviation values? Add all seven numbers: 7 + 4 + 1 + 1 + 2 + 4 + 5 = 24 How do we determine the mean of the absolute deviation values? Find the sum and divide by the number of values. 24 7 = 3.43 rounded to the nearest hundredth
Discovery Activity Extend the SOLVE Problem Determining the Mean Absolute Deviation Data Value Number of inches from Mean 7 4 1 1 2 4 5 Left or Right Positive or negative Negative Negative Negative Positive Positive Positive Positive Deviation from Mean Absolute Deviation -7 -4 -1 1 2 4 5 Left Left Left Right Right Right Right 7 4 1 1 2 4 5 48 51 54 56 57 59 60 24 Total of absolute deviation values MAD (mean absolute deviation) 3.43
Discovery Activity Extend the SOLVE Problem Determining the Mean Absolute Deviation The MAD (mean absolute deviation) for the data set is 3.43. This means that on average, the arm span of the students varies 3.43 inches from the mean of 55 inches.
Discovery Activity Extend the SOLVE Problem Determining the Mean Absolute Deviation What does the mean show us? The mean gives the measure of center of the data set with a single number. What does the MAD show us? The mean absolute deviation describes how the data values vary from the mean with a single number.
SOLVE DETERMINING THE MEAN ABSOLUTE DEVIATION
SOLVE During the math unit on measurement, Mr. Tomas also had students collect information about foot length. The foot lengths of the eight students are listed below. Foot length of eight students in inches: 1 1 1 12 ,13 ,14 ,14,15,12,11 ,11 2 2 2 1 2 What are the mean and the MAD of the data set for the foot length of the eight students? Explain what each value means for the data set. S Study the Problem Underline the question. This problem is asking me to find the mean and MAD of the foot lengths of the eight students and explain what each term means for the data set.
During the math unit on measurement, Mr. Tomas also had students collect information about foot length. The foot lengths of the eight students are listed below. Foot length of eight students in inches: 1 1 1 12 ,13 ,14 ,14,15,12,11 ,11 2 2 2 1 2 What are the mean and the MAD of the data set for the foot length of the eight students? Explain what each value means for the data set. O Organize the Facts Identify the facts. Eliminate the unnecessary facts. List the necessary facts. Foot length of eight students in inches: 1 2 1 2 1 2 1 2 12 ,13 ,14 ,14,15,12,11 ,11
L Line Up a Plan Write in words what your plan of action will be. Mean: Find the sum of the values and then divide by the number of values to determine the mean. Choose an operation or operations. Mean: addition, division
L Line Up a Plan Write in words what your plan of action will be. MAD: Put the scores in order from least to greatest. Place the values on a number line. Mark the mean on the number line. Count the number of spaces from each value to the mean and chart the absolute deviation for each. Find the total of the values for absolute deviation and divide by the number of values in that column to determine the MAD. Choose an operation or operations. MAD: addition, division
