Transcript MEAN - Bibb County Schools

Bellwork August
Copy and answer.
The data shows the ages of some dirt bike riders in an
AMA Supercross Race. Put them in order from least
to greatest.
17, 17, 19, 21, 22, 30, 19, 18, 19, 27, 29, 29, 16, 20
1. Make a stem-and-leaf plot of the data. How many riders
are over the age of 20?
2. Make a line plot of the data. What age occurs most
often?
Unit 1
Chapter 7
Section 2
Pg. 381
Mean, Median, Mode, and Range
with and without Outliers
Essential Questions:
• How does finding the measure of
central tendency help in
analyzing data?
• What is central tendency?
Mean, Mode, and Median
http://www.youtube.com/watch?v=FDzwnoXZQZY
Definitions
range: the difference between the highest
and lowest numbers in the set of data
mean: the average number of the set of data
median: the middle number in a set of
data after the numbers are arranged in order
from least to greatest
mode: the number that occurs the most in
a set of data
Definitions continued…
outlier: a number that is much smaller or
much larger than the set of data
35, 38, 27, 12, 30, 41, 31, 35
x
x
10
12
14
16 18
20
22
24
x
x
xx
26 28 30
32
34
x
36
x
38 40
42
Vocabulary Study List
(see your handout)
Vocabulary Word
Keyword
Picture
Definition
mean
the average
number of a set of
data
median
the middle number after
the numbers are arranged
in order from smallest to
largest
the number that occurs
the most in a set of data
mode
range
the difference
between the
highest and lowest
numbers in a set of
data
outlier
A number that is much
smaller or larger than the
other numbers in a set of
data
Babe Ruth Central Tendency and Variability Video Clip (3:45)
http://player.discoveryeducation.com/index.cfm?guidAssetId=a87b1f07-3e9e-4934-a26d-18125db4ea72
Write down 3 facts about Central Tendency.
Range!
How to find the range:
1. Arrange the numbers in ascending
order
2. Pick out the smallest number and
the largest number.
3. Subtract the two numbers.
Example 1:
Find the range of the data set.
4, 7, 8, 2, 1, 2, 4, 2
1, 2, 2, 2, 4, 4, 7, 8
8– 1 = 7
•MEAN
ACTIVITY 1
• Using interlocking number cubes, make 3
towers.
–6
–4
–8
• Now, figure out how to make them all the
same length.
Activity 1, ctd.
• If you moved two cubes from the tallest tower
and added them to the smallest tower, now
how long are all three towers?
• 6
• This is the MEAN. The mean of {8, 4, 6} is 6.
Activity 2
• Let’s find Mean another way.
• Data Set { 1, 3, 5, 9}
• Use interlocking cubes to make a tower for
each number.
Activity 2, ctd.
• Step 1: Find the SUM
• Combine all the cubes from all the towers to add.
• How many are their total?
• Step 2: Divide
• There were originally 4 towers, so divide the cubes into
four EQUAL groups.
• How many cubes are in each group?
– This is your MEAN.
How do you find the mean?
1. Add all the numbers together to
get the sum
Divide the sum by the number of
SIT DOWN!
items in the data set.
2.
Mr. Grumpy
Today’s Assignment:
Find the mean of:
2, 7, 9, 15, 12
GET QUIET!
NO GUM!
ZERO FOR YOU!
Example 2:
Find the mean of the following data set.
6, 4, 3, 5, 2, 5, 1, 8
6 + 4 + 3 + 5 + 2 + 5 + 1 + 8 = 34
8 items
sum
34  8 = 4.25
Mean Practice
• Complete the ‘No Rest for the Weary’ WS
• Show all work on a separate sheet of paper.
•MODE
How to find the mode?
Search to find the number
that occurs the most.
Sometimes it could be
more than one number.
Example 3:
Find the mode of the data set.
4, 7, 8, 2, 1, 2, 4, 2
1, 2, 2, 2, 4, 4, 7, 8
Activity 3
• Name Lengths/Singers of Bands
• Using the worksheet provided by your teacher,
we will cut strips of paper and fold them in
half to represent the MEDIAN.
How to find the median?
1. Arrange the numbers in order from least to
greatest.
2. Count until you find the middle number. If
you have one number, then you have found
the answer. If you have two numbers, then
continue to step 3.
3. Add the two numbers together, then divide
by 2
Median or
middle of the
street
Example 4:
Find the median of the data set.
4, 7, 8, 2, 1, 2, 4, 2
1, 2, 2, 2, 4, 4, 7, 8
2+4=6
62=3
Example 5:
Find the median of the following data set.
6, 4, 3, 5, 2, 5, 1, 8
1, 2, 3, 4, 5, 5, 6, 8
4+5=9
9  2 = 4.5
Mean, Median, and Mode
Brain-Pop
Write down 2 facts about mean, median, and
mode from the clip.
Work Session
• Find the mean, median, and mode for each
problem on the handout.
• Show all work.
• Remember the following:
– Mean: add up all of the numbers and divide them
by how ever many numbers are in the data set
– Median: put the numbers in order from least to
greatest and then find the number in the middle
– Mode: the number that occurs the most
Example 6: (Word Problem)
The line plot shows the number of dollars each of the 10 members of the
cheerleading team raised in a week. Which measure of central tendency
best describes this data? Justify your answer.
X
X
X X
X X
10
20
X
30
40
50
X
X
X
60
70
15 + 15 + 15 + 15 + 20 + 20 + 40 + 60 + 60 + 70= 330
10
= 33
10
The mode is 15. The mode focuses
on one data value and does not
describe the data set.
The median is 20. The median
best describes the data set
because it is closest to the
Most of the cheerleaders raised less than
amount most cheerleaders
$33, so the mean does not describe the
raised.
data set.
Outliers (9:56)
http://player.discoveryeducation.com/index.cfm?guidAssetId=4D5934D9-3890-4983-A91811B91F11C2AA&blnFromSearch=1&productcode=US
Write down 3 facts about outliers.
Example 7:
The data shows Sara’s scores for the last 5 math tests: 88, 90,
55, 94, and 89. Identify the outlier in the data set. Then
determine how the outlier affects the mean, median, and
mode of the data. Then tell which measure of central
tendency best describes the data with the outlier.
55, 88, 89, 90, 94
mean:
outlier
median:
55+88+89+90+94= 416 55, 88, 89, 90, 94
416  5 = 83.2
The mean is 83.2.
The median is 89.
With the Outlier
55
mode:
There is no
mode.
Example 7:
The data shows Sara’s scores for the last 5 math tests: 88, 90,
55, 94, and 89. Identify the outlier in the data set. Then
determine how the outlier affects the mean, median, and
mode of the data. Then tell which measure of central
tendency best describes the data with the outlier.
55, 88, 89, 90, 94
outlier
mean:
median:
88+89+90+94 = 361
88, 89,+90, 94
2
= 89.5
The median is
89.5.
361  4 = 90.25
The mean is 90.25.
Without the Outlier
55
mode:
There is no
mode.
Compare data with & without data
With the Outlier
The mean is 83.2.
The median is 89.
There is no mode.
Without the Outlier
The mean is 90.25.
The median is 89.5.
There is no mode.
The mean between the two are 7.05. The
median changes .5. Taking out the outlier
only changes the mean dramatically.
Possible Activities
• See the next few slides
Mean, Median, Mode, Range and
Outliers with M&Ms
• Open your bag of
M&Ms.
• Count how many
M&Ms are in your bag
(DO NOT EAT ANY YET)
• We will compare how
many M&Ms are in the
bags of of your
classmates.
• Fill in your chart.
Person
# of M&M’s in Their Bag
•Find the mean, median, and mode of the number of
M&Ms in the bags.
•Are there any outliers?
•What is the range?