Transcript Unit 10: Statistics

EXPLORING descriptions of
SPREAD
UNIT 13
Describing Data
There are two ways to describe a set of data:
• Graphically
Dot plot – Bar Graph – Histogram – Boxplot
• Numerically-using a single number to describe
the relationship of the data
– Measures of Center: Mean and Median review
these descriptions in your notes
– Measures of SpreadToday we will focus on the numerical descriptions
Measures of Spread describe
how much values typically vary
from the center
These measures are:
• Range – a description of how far apart the distance
from the highest to lowest data pieces; found using
highest minus lowest data
• Interquartile Range (IQR) – a description of the
middle 50% of the data ; found using Q3 – Q1
• Mean Absolute Deviation briefly view description in your
notes and then continue with the PPT.
Now let’s explore
“deviations from the mean”
as a way to determine how
accurately the mean may
describe “typical”.
Thinking about the Situation
Consider the following test scores:
Student
Test 1
Test 2
Test 3
Test 4
Li
65
82
93
100
Bessie
82
86
89
83
Jamal
80
99
73
88
Who is the best student? How do you know?
Take a few minutes to decide with your partner
So with all students having the
same mean, let’s see if we can dig
a little deeper in our comparison.
The MEAN ABSOLUTE DEVIAITON
(MAD) will help us. Let’s take a
few minutes to explore MAD.
Mean Absolute Deviation (MAD)
Add to notes
STEP 1: Find the mean
STEP 2:
Subtract the mean from
each piece of data
STEP 3: Find the absolute
value of each difference
STEP 4: Find the mean of the new
differences (deviations)
NOW WE WILL TRY THIS METHOD.
Mean Absolute Deviation
Write the list of numbers shown on the
number line and then find the Mean
Absolute Deviation
0
1
2
3
4
5
6
7
8
9
STOP AND COMPLETE CHART on NOTES
10 11
So what exactly is deviation?
-4
-3
+5
-1
0
1
2
3
4
+3
5
6
7
8
9
x
(-4) + (-3) + (-1) = -8
(+5 ) + (+3) = +8
10 11
Mean Absolute Deviation
-3.2
0
1
2
3
+3.2
4
5
6
7
8
9
10 11
x
Notice that our Mean Absolute Deviation or MAD
was 3.2 and most of our original data does fall
within plus or minus 3.2 points of the mean of 5.
Highlight the following in your notes:
A low mean absolute deviation indicates
that the data points tend to be very close
to the mean and not spread out very far
so the mean is an accurate description of
“typical”, and a high mean absolute deviation
indicates that the data points are spread out
over a large range of values.
Now take a few minutes to go back to
our original question about the best
student. Find the MAD score for each
student and then make a decision
based on all of your data about the
best student. Be prepared to discuss.
Student
Test 1
Test 2
Test 3
Test 4
Li
65
82
93
100
Bessie
82
86
89
83
Jamal
80
99
73
88
Now you try the CLASSWORK
found on your handout.
When you and your partner have
completed the work individually,
check to see if you agree.
We will review this section
together in a few minutes