Mean, Median, Mode

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Mean, Median, Mode Range
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Outlier

• An outlier is a data item that is much higher or
  much lower than items in a data set.
• 1, 2, 5, 27, 3, 4

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Vocabulary Review

• Sum the answer to an addition problem.
• Addend the numbers you added together to get
  the sum.

6 9 15
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Definition

• Mean the average of a group of numbers.

2, 5, 2, 1, 5
Mean 3
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Mean is found by evening out the numbers
2, 5, 2, 1, 5
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Mean is found by evening out the numbers
2, 5, 2, 1, 5
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Mean is found by evening out the numbers
2, 5, 2, 1, 5
mean 3
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How to Find the Mean of a Group of Numbers

• Step 1 Add all the numbers.

8, 10, 12, 18, 22, 26
81012182226 96
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How to Find the Mean of a Group of Numbers

• Step 2 Divide the sum by the number of addends.

8, 10, 12, 18, 22, 26
81012182226 96
How many addends are there?
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How to Find the Mean of a Group of Numbers

• Step 2 Divide the sum by the number of addends.

1
6
6)
96
sum
of addends
6
3
6
6
3
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How to Find the Mean of a Group of Numbers
You try this one

• The mean or average of these numbers is 16.

8, 10, 12, 18, 22, 26
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What is the mean of these numbers?
7, 10, 16
11
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What is the mean of these numbers?
2, 9, 14, 27
13
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What is the mean of these numbers?
26, 33, 41, 52
38
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Definition

• Median the middle number in a set of ordered
  numbers.

1, 3, 7, 10, 13
Median 7
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How to Find the Median in a Group of Numbers

• Step 1 Arrange the numbers in order from least
  to greatest.

21, 18, 24, 19, 27
18, 19, 21, 24, 27
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How to Find the Median in a Group of Numbers

• Step 2 Find the middle number.

21, 18, 24, 19, 27
18, 19, 21, 24, 27
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How to Find the Median in a Group of Numbers

• Step 2 Find the middle number.

18, 19, 21, 24, 27
This is your median number.
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How to Find the Median in a Group of Numbers

• Step 3 If there are two middle numbers, find
  the mean of these two numbers.

18, 19, 21, 25, 27, 28
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How to Find the Median in a Group of Numbers

• Step 3 If there are two middle numbers, find
  the mean of these two numbers.

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21 25
median
23
2)
46
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What is the median of these numbers?
16, 10, 7
7, 10, 16
10
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What is the median of these numbers?
29, 8, 4, 11, 19
4, 8, 11, 19, 29
11
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What is the median of these numbers?
31, 7, 2, 12, 14, 19
2, 7, 12, 14, 19, 31
13
2)
12 14 26
26
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Definition

• A la mode the most popular or that which is in
  fashion.

Baseball caps are a la mode today.
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Definition

• Mode the number that appears most often in a
  set of numbers.

1, 1, 3, 7, 10, 13
Mode 1
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How to Find the Mode in a Group of Numbers

• Step 1 Arrange the numbers in order from least
  to greatest.

21, 18, 24, 19, 18
18, 18, 19, 21, 24
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How to Find the Mode in a Group of Numbers

• Step 2 Find the number that is repeated the
  most.

21, 18, 24, 19, 18
18, 18, 19, 21, 24
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Which number is the mode?
29, 8, 4, 8, 19
4, 8, 8, 19, 29
8
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Which number is the mode?
1, 2, 2, 9, 9, 4, 9, 10
1, 2, 2, 4, 9, 9, 9, 10
9
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Which number is the mode?
22, 21, 27, 31, 21, 32
21, 21, 22, 27, 31, 32
21
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Definition

• Range the difference between the greatest and
  the least value in a set of numbers.

1, 1, 3, 7, 10, 13
Range 12
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How to Find the Range in a Group of Numbers

• Step 1 Arrange the numbers in order from least
  to greatest.

21, 18, 24, 19, 27
18, 19, 21, 24, 27
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How to Find the Range in a Group of Numbers

• Step 2 Find the lowest and highest numbers.

21, 18, 24, 19, 27
18, 19, 21, 24, 27
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How to Find the Range in a Group of Numbers

• Step 3 Find the difference between these 2
  numbers.

18, 19, 21, 24, 27
27 18 9
The range is 9
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What is the range?
29, 8, 4, 8, 19
4, 8, 8, 19, 29
29 4 25
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What is the range?
22, 21, 27, 31, 21, 32
21, 21, 22, 27, 31, 32
32 21 11
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What is the range?
31, 8, 3, 11, 19
3, 8, 11, 19, 31
31 3 28
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What is the range?
23, 7, 9, 41, 19
7, 9, 23, 19, 41
41 7 34
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17, 18, 19, 21, 24,26, 27
The lower quartile (LQ) is the median of the
lower half of the data.
The LQ is 18.
The upper quartile (UQ) is the median of the
upper half of the data.
The UQ is 26.
The interquartile range is UQ-LQ
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Even amounts divide in 2 equal halves.
13,15,18,19,22,25
L.Q.
U.Q.
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Key Skills
TRY THIS
Use data to construct a histogram.
Jose bowled 11 games 172, 152, 168, 157,143,
175,144, 164, 142, 172, 168.
Histogram
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Find the median
76, 78, 82, 87, 88, 88, 89, 90, 91, 95
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Find the median of this segment
Find the median of this segment.
82
90
76,78, 82
88, 89,90
3rd quartile
1st quartile
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End of 1st quartile
Median
Minimum
End of 3rd quartile
Maximum
76, 78, 82, 87, 88, 88,
89, 90, 91, 95
75
80
100
70
85
105
90
95
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Now for the box and whisker
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Find the median
142, 143, 144, 152, 157, 164, 168, 168, 172, 172
175.
164
Find the median of this segment
Find the median of this segment.
144
172
142, 143, 144
168, 168, 172
3rd quartile
1st quartile
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End of 1st quartile
Median
Minimum
End of 3rd quartile
Maximum
142, 143, 144, 152, 157, 164, 168, 168,
172, 172, 175.
150
155
175
145
160
180
165
170
140
Now for the box and whisker
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Rules and Properties
Data Displays
A box-and-whisker plot shows how data is
distributed by using the median, upper and lower
quartiles, and the greatest and least values in
the data set.
1. Draw a number line and identify the median and
the greatest and least values with vertical lines.
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Rules and Properties
Data Displays
A box-and-whisker plot shows how data is
distributed by using the median, upper and lower
quartiles, and the greatest and least values in
the data set.
2. Identify the lower quartile with a vertical
line. The lower quartile is the median of all
data in the lower half (below the median) of the
data set.
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Rules and Properties
Data Displays
A box-and-whisker plot shows how data is
distributed by using the median, upper and lower
quartiles, and the greatest and least values in
the data set.
3. Identify the upper quartile with a vertical
line. The upper quartile is the median of all
data in the upper half (above the median) of the
data set.
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Rules and Properties
Data Displays
A box-and-whisker plot shows how data is
distributed by using the median, upper and lower
quartiles, and the greatest and least values in
the data set.
4. Draw a rectangular box from the lower quartile
to the upper quartile. 5. Draw lines from the
ends of the box to the marks for the greatest and
least values.
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Key Skills
Use data to construct stem-and-leaf plots,
histograms, and box-and-whisker plots.
Ten students had the following test scores on a
math test 88, 78, 82, 95, 90, 91, 87, 76, 88, 89.
Box-and-whisker plot
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Rules and Properties
Mean sum of all elements divided by the total
number of elements.
Median middle number in a set when the elements
are placed in numerical order. If there are an
even number of elements, the median is the
average of the two middle numbers.
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Rules and Properties
Mode the element that occurs most often. There
may be no mode, one mode, or several modes.
Range difference between the greatest and least
values in a set.
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Key Skills
Find the mean, median, mode, and range for a set
of data.
In one season, professional baseball teams in one
division had 91, 78, 73, 73, and 66 wins.
median Arrange the data in order 66, 73, 73,
78, 91
mode 73 (73 occurs twice in the set)
range 91 66 25
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Key Skills
A quiz was given in Mr. Cuccis Algebra Class
with the following results.
7, 10, 10, 9, 8, 9, 7, 4, 3, 7, 10, 4, 8, 9, 6,
7, 10
Create a frequency table, find the mean, mode,
median and range.
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Construct a Frequency Table (tally sheet)
7, 10, 10, 9, 8, 9, 7, 4, 3, 7, 10, 4, 8, 9, 6,
7, 10
Enter the data value into the 1st column
Data Value Tally Frequency
0
1
2
3
4
5
6
7
8
9
10
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Construct a Frequency Table (tally sheet)
7, 10, 10, 9, 8, 9, 7, 4, 3, 7, 10, 4, 8, 9, 6,
7, 10
Enter a tally for each entry.
Data Value Tally Frequency
0
1
2
3
4
5
6
7
8
9
10
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Construct a Frequency Table (tally sheet)
In this way the mode and the median can easily be
seen.
Count the tallies and put the total for each
value in the frequency column
Data Value Tally Frequency
0
1
2
3
4
5
6
7
8
9
10
1
2
1
4
2
3
4
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Introduction

• Using statistics is a helpful way to study
  different situations. Today I will demonstrate
  how to find the mean, median, and mode of a set
  of numbers.

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Topics of Discussion

• The mean (or average) is found by taking the sum
  of the numbers and then dividing by how many
  numbers you added together.
• The number that occurs most frequently is the
  mode.
• When the number are arranged in numerical order,
  the middle one in the mean.

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Topic One

• The mean (or average) is found by adding all the
  numbers and then dividing by how many numbers you
  added together.
• Example 3,4,5,6,7
• 34567 25
• 25 divided by 5 5
• The mean is 5

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Topic Two

• The number that occurs most frequently is the
  mode.
• Example 2,2,2,4,5,6,7,7,7,7,8
• The number that occurs most frequently is 7
• The mode is 7

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Topic Three

• When numbers are arranged in numerical order, the
  middle one is the median.
• Example 3,6,2,5,7
• Arrange in order 2,3,5,6,7
• The number in the middle is 5
• The median is 5

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Averaging Grades

• Lowest
• 55
• 60
• 75
• 80
• 80
• 80
• 83
• 83
• 93
• 93
• 93
• 93
• 93
• Highest

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Find The mean of the following set of grades

• Lowest
• 55
• 60
• 75
• 80
• 80
• 80
• 83
• 83
• 93
• 93
• 93
• 93
• 93
• Highest

• First add all the grades together.
• The total equals 1061
• Now divide 1061 by 13 (total grades
• The answer is 81.61
• The mean is 81.61

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Find the median of the following numbers

• Lowest
• 55
• 60
• 75
• 80
• 80
• 80
• 83
• 83
• 93
• 93
• 93
• 93
• 93
• Highest

• The median is the number in the middle of numbers
  which are in order from least to greatest.
• If we count from both sides the number in the
  middle is 83.
• The median is 83

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Find the mode of the following grades

• Lowest
• 55
• 60
• 75
• 80
• 80
• 80
• 83
• 83
• 93
• 93
• 93
• 93
• 93
• Highest

• The mode is the number which occurs most often.
• The number which occurs most often is 93
• The mode is 93

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Real Life

• If these were your math grades, what would you
  learn by analysising them?
• The mean was 81.61. In order to raise your
  grades, you would have to make higher than an
  81.61 on the rest of your assignments.
• The mode was 93 which was your highest grade.
  You could look at these papers to see why you
  made this grade the most.
• The median is a 83. This means that most of your
  grades were higher than your average. Find your
  week area and try to improve.

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Real Life

• Real Life
• Knowing the mean, median, and mode will help you
  better understand the scores on your report card.
  By analyzing the data (grades) you can find your
  average, the grade you received most often, and
  the grade in the middle of your subject area.
• Better understanding your grades may lead to
  better study habits.

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Mean, Median, Mode Range
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