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Essential Question: How do you
compare measures of central
tendency and dispersion?
Before we
start…
The data shown below represents the
weights (in pounds) of 9 dogs at a kennel.
Write the data in order from least to greatest
32, 12, 15, 25, 18, 40, 18, 29, 27
What data value occurs most?
Which weight is in the middle when
the data is listed in order?
What are the measures
of central tendency?
They are used to
represent a
typical number
in a data set.
Mean
Median
Mode
What is the mean?
The average of a
numerical data set.
Add up all the data points
and divide by the number of
data.
𝒙 is the symbol for mean.
What is the median?
The middle number
when the values are
written in numerical
order.
If there is an even number of
values, the median is the
mean of the two middle
values.
What is the mode?
The value that occurs most
frequently.
No mode
One mode
More than
one mode
What should you choose the
measure of central tendency?
Type
When Best Used
Mean
The data sets have no outliers
Median
The data set has outliers, but there are no
big gaps in the middle of the data
Mode
The data set has many repeated numbers
The data shown below represents the weights (in
pounds) of 9 dogs at a kennel. Which measure of
central tendency best represents the data?
32, 12, 15, 25, 18, 40, 18, 29, 27
The heights (in feet) of 8 waterfalls in the state
of Washington are listed below. Which measure
of central tendency best represents the data?
1000, 1000, 1181, 1191, 1200, 1268, 1328, 2584
The lengths (in miles) of the 10 longest rivers in
the U.S. are listed below. Which measure of
central tendency best represents the data?
1290, 1310, 1420, 1450, 1460, 1900, 1900, 1980,
2340, 2540
Archmont High School is collecting recyclable paper as
a fundraiser to buy some benches for the courtyard. The
newspapers are gathered into 5-inche bundles. Ms. Sato
counted the bundles received each Friday for the first
quarter of the school year. Which measure of central
tendency best represents the data?
15, 12, 14, 15, 18, 15, 13, 14, 13, 12
A sub shop adds a new bread to its menu. To see if they
should keep it, the manager counts how many orders of
that bread type are taken each day. Which measure of
central tendency best represents the data?
10, 16, 14, 13, 17, 15, 18, 16, 19
What is a measure of
dispersion?
It describes the
dispersion, or spread, of
data.
Range
Mean Absolute
Deviation
What is the range?
The difference of the greatest
value and the least value.
Gives the length of the
interval containing the
data.
What is the mean absolute deviation?
Gives the average
variation of the data
from the mean.
You find the average
of how far away each
data value is from the
mean of the set.
Mean Absolute Deviation Formula
x1  x  x2  x  ...  xn  x
n
How do you find the mean absolute
deviation?
• Find the mean.
• Find the distance between each data point and
the mean.
• Add the distances up.
• Divide by the number of values in the data set.
Marketing Each person that visited the Comic Book
Shoppe’s web site was asked to enter the number of
times each month they buy a comic book. They received
the following responses one day:
2, 2, 3, 4, 14
Find the range and the mean absolute deviation.
Dances The prom committee kept count of how many
tickets it sold each day during lunch:
12, 32, 36, 41, 22, 47, 51, 33, 37, 49
Find the range and the mean absolute deviation.
Financial Literacy Mike is waiting tables at the Pizza
Pan Restaurant. He is keeping track of the tips that he
receives each hour.
20, 31, 24, 22, 35, 12
Find the range and the mean absolute deviation.
Parties Dalila kept an account of what each cousin
spent on their grandmother’s birthday party:
25, 24, 36, 28, 34, 25, 17
Find the range and the mean absolute deviation.
How do you compare measures of…
Central tendency?
To find which measure best
represents most of the data.
Dispersion?
To find which data set covers a
wider interval.
Mean
Median
Mode
Range
Mean Absolute
Deviation
How do you compare measures of central
tendency and dispersion?
Ticket Out the Door
Find the mean, median, mode, range and mean
absolute deviation of the data.
13, 16, 19, 20, 22, 25, 30, 31