Download Variance, Mean Absolute and Standard Deviation PowerPoint

Variation, Mean Absolute and
Standard Deviation (12-3)
Objective: Calculate and interpret variation in real
world context through the use of mean absolute
deviation, standard deviation, and variance.
Statistical Analysis
Data that involve only one variable are
called univariate data.
 This kind of data can be represented by
measures of central tendency, such as the
mean, median, and mode.
 Univariate data can also be represented
by measures of variation, such as range,
quartiles, and interquartile range.

Statistical Analysis
Type
Range
Quartile
Description
When Best Used
The difference between
the greatest and least
values.
To describe which
numbers are included in
the data set.
The values that divide the
data set into four equal
parts.
To determine values in the
upper and lower portions
of a data set.
The range of the middle
To determine what values
half of a data set; the
Interquartile Range
lie in the middle half of
difference between the
the data set.
upper and lower quartiles.
Statistical Analysis
The mean absolute deviation is the
average of the absolute values of the
differences between the mean and each
value in the data set.
 Recall that absolute value makes all
numbers positive.
(| x   |)

 Mean Absolute Deviation =
n

Example 1

A rescue agency records the number of
pets adopted each month: 14, 18, 12, 17,
15, 20. Find the mean absolute deviation.
Steps for Calculating Mean Absolute
Deviation
1.
2.
3.
4.
Go to STAT on your calculator and
choose 1:Edit.
Enter your data into L1.
Go to STAT, right arrow over to CALC,
and choose 1:1-Var Stats. Press ENTER.
Find the mean (x). For Mean Absolute
Deviation, we will call this μ.
Example 1

A rescue agency records the number of
pets adopted each month: 14, 18, 12, 17,
15, 20. Find the mean absolute deviation.
◦ μ = 16
Steps for Calculating Mean Absolute
Deviation
5.
6.
Go to STAT and choose 1:Edit.
Scroll up so that L2 is highlighted. Enter
the expression |x – μ| by pressing
MATH, right arrowing over to NUM, and
choosing 1:abs(. Follow that with L1
minus the number you found for μ in
step 4 and close the parenthesis. Press
ENTER and L2 will automatically be filled
in with data values.
Steps for Calculating Mean Absolute
Deviation
7.
8.
9.
Go to STAT, right arrow over to CALC,
and choose 1:1-Var Stats. Press L2
before you press ENTER.
Find the Σx value and the n value.
Calculate the Mean Absolute Deviation
by  x
n
Example 1

A rescue agency records the number of
pets adopted each month: 14, 18, 12, 17,
15, 20. Find the mean absolute deviation.
◦ μ = 16
◦ Σx = 14
◦n=6
Mean Absolute Deviation = 2.3
x
14

◦.

n
6
Check Your Progress

Choose the best answer for the following.
◦ Giles and his father record the number of
catfish they catch each month out of the river
behind their house: 6, 8, 10, 4, 5, 9. Find the
mean absolute deviation.
A.
B.
C.
D.
12
7
2.5
2
μ=7
Σx = 12
n=6
MAD = 12/6
Standard Deviation





The standard deviation is a calculated value
that shows how the data deviates from the
mean of the data.
The standard deviation is represented by the
lower-case Greek symbol sigma, σ.
2
(x


)
Standard Deviation = 
n
The variance of the data is the square of the
standard deviation.
Variance is represented by σ2.
Example 2

Find the mean, variance, and standard
deviation of 5, 7, 8, 14, 16.
◦ μ = 10
◦ σ = 4.2
◦ σ2 = 17.64
Check Your Progress

Choose the best answer for the following.
◦ Find the variance and standard deviation of 22,
24, 19, 18, 17.
A.
B.
C.
D.
8.3; 2.9
6.8; 2.6
5.4; 2.3
3.4; 5.8
Standard Deviation
The standard deviation illustrates the
spread of the data.
 For example, when the mean is 75 and
the standard deviation is 3, we know that
almost all of the data values are very
close to the mean.
 When the mean is 75 and the standard
deviation is 15, then the data are more
spread out and there may be an outlier.

Example 3

Daisy kept track of the number of text
messages she sent each month for 6
months. Find the standard deviation of
the data set.
Month
Messages
January
985
February
1005
March
1100
April
950
May
1200
June
1010
σ = 84.1
Check Your Progress

Choose the best answer for the following.
◦ The city of Hardesty keeps track of the
number of fans the local baseball team draws
to the games each month. Find the standard
deviation of the data set.
Month
Baseball Fans
A.
B.
C.
D.
194.3
205.1
168.1
167.3
January
965
February
805
March
1120
April
1006
May
1225
June
1310