Download Mean Deviation - Effingham County Schools

Unit 4
Variance & mean deviation
Frequency Distribution
Golden Ratio
Dot Plots
How do you calculate the
variance and mean
deviation for a data set?
M2 Unit 4: Day 4
Variance


Variance can be found by squaring the
standard deviation.
If you have a sample of data:
2
variance = S

If you have data for a population:
variance = s
2
Variance Example 1
A sample of test scores is as follows:
67, 95, 74, 86, 80, 70
Find the variance.
2
variance = S
2
S x » 10.5388 = 10.5388 » 111.066
Variance Example 2
A sample of driving speeds is as follows:
55, 62, 59, 68, 75, 70
Find the variance.
2
variance = S
Variance Example 3
Find the variance: 19,8,12,17,16,25,5
variance = s
s x = 6.3
2
variance = s x
2
s x = 39.7
2
Variance Example 4
Find the variance: 38,42,40,37,28,39,40
variance = s
2
Using Variance to find Standard
Deviation
If you know the variance
s
2
or S
2
then you can find the s.d.
s or S
by taking the square root.
Example 1
If the Variance = 125. Find the standard deviation.
variance = 125
SD = 125
SD » 11.1803
Example 2
If the Variance = 52. Find the standard deviation.
variance = 52
SD = 52
SD » 7.2111
Mean Deviation


The Mean Deviation (MD) is the mean of the
distances between each value and the mean.
It gives us an idea of how spread out from
the center the set of values is.
n
MD =
åi
xi - x
=1
n
ACTUAL VALUE - MEAN
NOT IN CALCULATOR;
ON FORMULA SHEET
Watch me as I work one…

The ECHS soccer team played 3 games last
weekend. The number of points scored in each
game was 11, 8, 8. Find the mean deviation.
x=9
• First, find the mean, x
• Then, find the difference of each data value and the
mean
• Last, find the sum of the numbers you just found
and divide by the number of terms in the data set.
11- 9 = 2
8- 9 = 1
8- 9 = 1
2+ 1+ 1 4
= = 1.3
3
3
MD = 1.3
Let’s try one together…
1. The ECHS baseball team played 4 games last week.
The number of points scored in each game was 8,
12, 10, 7. Find the mean deviation.
• First, find the mean, x x = 9.25
• Then, find the difference of each data value and the
mean
• Last, find the sum of the numbers you just found
and divide by the number of terms in the data set.
8 - 9.25 = 1.25
12 - 9.25 = 2.75
10 - 9.25 = .75
7 - 9.25 = 2.25
1.25 + 2.75 + .75 + 2.25 7
= = 1.75
4
4
MD = 1.75
You try…
2. A student took 5 exams in a class and had
scores of 92, 75, 95, 90, and 98. Find the
mean deviation for her test scores.
x = 90
5
MD =

åi
xi - x
=1
5
2 + 15 + 5 + 0 + 8 30
=6
=
=
5
5
We can conclude that on average, this
student’s scores deviated by 6 points from
the mean.
MD =
You try…
3. The JV football team played 7 games this
season. Find the mean deviation of the number
of points they scored in each game.
x = 15
11,15,17,20,13,11,18
7
åi
=1

xi - x
4 + 0 + 2 + 5 + 2 + 4 + 3 20 = 2.9
=
=
7
7
7
On average, the # of points scored in each
game deviated 2.9 points from the mean.
Frequency Distribution


A frequency distribution lists the value with
its associated frequency.
EX 1: The following is the number of hours students
study per night: 1,1,1,1,2,2,2,3,3,3,4,4,5
Create a frequency distribution.
Create a frequency distribution
2. Use the following data:
8, 7, 5, 8, 5, 7, 6, 5, 5, 8, 6, 7, 8
Mark
5
6
7
8
Tally
IIII
II
III
IIII
Count
4
2
3
4
Use the frequency table below to
find the mean and standard
deviation
Mark
3
5
9
10
13
Tally
III
III
IIII
II
I
x = 7.15
s = 3.16
Count
3
3
4
2
1
Dot Plot


A dot plot is a type of graphic display
used to compare frequency counts within
categories or groups.
As you might guess, a dot plot is made
up of dots plotted on a graph. Here is
how to interpret a dot plot.
#1 - find the mean, standard
deviation and mode for the given
data
Dot Plot
Collection 1
10.68
mean:_______
4.49
standard deviation:_________
0
2
4
6
8
10 12
x
14 16 18
20 22
10
Mode: _______
#2 – find the mean, standard
deviation and mode for the given
data , then create a frequency table
Histogram
Collection 1
43.81
mean:_______
6
4.05
standard deviation:_________
5
Count
4
39, 40
Mode: ________
3
2
1
38
40
42
44
46
48
data
50
52
54
56
Golden Ratio

The golden ratio is
1+ 5
r=
» 1.6180339887
2
r (phi) is pronounced "fee" or "fi"


Artists and architects deem this ratio as being the
most aesthetically pleasing and have used it as a
basis for their art and buildings for years.
Famous examples: Mona Lisa, Sacrament of the
Last Supper, and the Parthenon in Athens.



Handout
Review sheet
STUDY FOR TEST Tuesday 