Chapter 3x - Holy Angels Elementary School

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CHAPTER 3
3-1 MEAN, MEDIAN, MODE, AND
RANGE
IWBAT compute the mean, median, mode, and
range from a data set
VOCABULARY

Mean – Average using division

Median – Average using the central number



Mode – Average using the number that occurs
most frequently
Range – How far is the data spread out
Measures of Central Tendency – The mean,
median, and mode. They indicate what is typical
of a set of data.
MEAN
Find the mean of the number of people at a play during 8
showings.
100, 100, 89, 90, 95, 100, 90, 104
1) Add all numbers in data set
100 + 100 + 89 + 90 + 95 + 100 + 90 + 104
768
2) Divide the sum by the
number of data in the set
768 ÷ 8
96
The Mean is 96
MEDIAN
Find the median of the number of people at a play during 8
showings.
100, 100, 89, 90, 95, 100, 90, 104
1) Write data in order from least 89 90 90 95 100 100 100 104
to greatest
2) Starting from opposite ends,
find the number(s) in the middle
*If there are two numbers
left in the middle: find the
mean of the two numbers
MODE AND RANGE
Find the mode of the number of people at a play during 8 showings.
100, 100, 89, 90, 95, 100, 90, 104
1) Mode: Which number(s)
occur the most frequently
100
Mode: 100
2) Range: Subtract lowest
number and the greatest
number
104 – 89 = 15
Range is 15
EXAMPLES
Find the mean, median, mode and range of the
following data set.
31, 25, 37, 25, 42
1) Mean
31 + 25 + 37 + 25 + 42
160
160 ÷ 5
32
2) Median
25 25 31 37 42
31
3) Mode
4) Range
25
42 – 25 = 17
INDEPENDENT PRACTICE
Find the mean, median, mode, and range of the
following data set.
35, 20, 7, 12, 35, 12, 9, 6
3-2 DATA WITH OUTLIERS
IWBAT compute the mean, median, mode, and
range of data sets with and without outliers to
determine their effect on central tendencies
VOCABULARY

Outlier – A number in a data set that is very
different from the rest of the numbers. Data sets
can have more than one outlier.
IDENTIFY THE OUTLIERS. THEN FIND THE
MEAN, MEDIAN, AND MODE WITH AND WITHOUT
THE OUTLIERS. ROUND MEAN TO THE NEAREST
TENTH.
15, 18, 12, 9, 46
1) Identify the outlier(s)
2) Find mean, median, mode
with outlier
46
Mean:
15+18+12+9+46
5
100
5
= 20
Median: 9 12 15 18 46
15
Mode: None
3) Find mean, median, and
mode without the outlier
Mean:
15+18+12+9
4
54
4
= 13.5
Median: 9 12 15 18
12 + 15
2
27
2
= 13.5
Mode: None
*How did the outlier effect the
mean? (Increase or decrease)
*How did the outlier effect
the median?
The mean was increased
by the outlier
The median was
increased by the outlier
EXAMPLE
Identify the outliers. Then find the mean, median, and mode of the
data with and without the outlier. Round the mean to the nearest
tenth.
25, 33, 28, 14, 35, 60
Outliers
14 and 60
With outliers
Mean: 25 + 33 + 28 + 14 + 35 + 60 = 195
195
= 32.5
6
Median: 14 25 28 33 35 60
28 + 33 = 61
Mode: None
61
= 30.5
2
Without outliers
Mean: 25 + 33 + 28 + 35 = 121
121
= 30.25 ≈ 30.3
4
Median: 25 28 33 35
28 + 33 = 61
61
= 30.5
2
Mode: None
*How did the outliers effect the
mean? (Increase or decrease)
The mean increased with the
outliers
*How did the outliers effect the
median?
The median was not effected by
the outliers
*How did the outliers effect
the mode?
The mode was not effected by the
outliers
3-3 STEM-AND-LEAF PLOTS
IWBAT use stem-and-leaf plots to analyze central
tendencies of data with 2 or 3 digit numbers
MAKING A STEM-AND-LEAF PLOT
Average Olympic Basketball Scores
Angola
Argentina Australia
Brazil
China
Croatia
56
70
96
92
72
85
Greece
Lithuania
Puerto
Rico
South
Korea
USA
Yugoslavi
a
80
85
89
81
104
96
1) Make a stem-and-leaf plot of the data
2) Use the stem-and-leaf plot to find the range, median, and mode.
EXAMPLE
Average June Temperature (°F) of Some Western US Cities
Albuquerque
75
Flagstaff
60
Missoula
59
Salt Lake City
67
Bismarck
65
Fort Worth
82
Portland
64
San Francisco
61
Boise
66
Lincoln
73
Rapid City
65
Seattle
60
1) Make a stem-and-leaf plot of the data.
2) Use the stem-and-leaf plot to find the range, median, and mode.
USING A STEM-AND-LEAF PLOT
Average Yearly Precipitation in Some US Cities (in Inches)
Stem
Leaf
4 1 1 2 3 5 7
5 1 4 4
1) Find the Range
2) Find the Median
3) Find the Mode
EXAMPLE
Heights of Buildings Downtown (in feet)
Stem
Leaf
2
3
4
5
6
7
8
9
10
11
12
5
2
0
2
2
3
5
0
3
5
6
1) Why is the leaf of stem 6 blank?
2) Find the range
3) Find the mode
5 8 8 9
5 5 9
2 3 8
4 7 8
5
1 4 4 7 8
5 9
8
3-4 CHOOSING THE BEST GRAPH
IWBAT choose the type of graph that best
describes a set of numerical data and
relationships.
TYPES OF GRAPHS
Bar Graph – shows specific number of multiple
groups (ex. Number of students in each class) can
also use a pictograph
 Double Bar Graph – compares and contrasts two
groups side-by-side (ex. Sports that girls play vs.
sports that boys play)
 Line Graph – shows changes over time or other
kinds of interrelationships (Ex. Temperatures
over a month, Population over several years)
 Circle Graph – Describes parts of a whole (Ex.
The percentage of students that like specific
types of music)

EXAMPLES
Community Theater Group
Year
# of Dramas # of Comedies
Attendance
Cost per Ticket
1996
10
8
6,500
$10.50
1997
15
7
4,000
$12.00
1998
12
9
5,500
$12.50
1999
12
10
8,000
$14.00
1) Which sets of data show totals for each year?
Number of dramas, number of comedies, and attendance
2) Which set of data shows a steady increase over time?
Cost per ticket
3) Which type of graph would be best for the data on the number of dramas
and
number
of comedies?
Why? the specific numbers of two groups
Double bar
graph, compares
4) Which type of graph would be best for the data on cost per
ticket?
Why?
Line graph, shows change of prices over several years
WHICH GRAPH SHOULD YOU USE?
1) You want to show that the music store sells about 4 times as many
country
music CDs as jazz CDs.
Bar Graph or Pictograph
2) You want to show that sales at the music store have been falling steadily
for the last three years.
Line Graph
3) You want to show that current sales of Elvis’ recordings are greater than
sales of the Beatles’ recordings.
Bar Graph or Pictograph
4) You want to show what part Oldies and Classic Rock CDs are of the
entire
collection of music in the store.
Circle Graph
3-5 UNDERSTANDING SAMPLING
IWBAT understand the use of sampling in
describing group tendencies.
VOCABULARY
Population – The entire group of people or things
being considered (Ex. All students at Holy
Angels, The entire bag of marbles)
 Sample – Part of the population (Ex. Girls at
Holy Angels, Only the 6th grade class, A handful
of marbles from the bag)
 Samples are used when studying or surveying
when the population is too difficult or impractical

EXAMPLE #1
There is a barrel of marbles. You want to know how many green
marbles are in the barrel. You scoop out a bucket of marbles.
1) What is the population?
The whole barrel of marbles.
2) What is the sample?
The bucketful of marbles.
You want to take two samples to estimate a central tendency.
Sample 1: There are 210 marbles in the bucket. Of those marbles, 51
are green.
1) Find the percentage
51

=
210 
51 ÷ 210 ≈ 0.24
24%
Sample 2: You scoop another bucketful. This time there are 188
marbles, 61 of those are green.
2) Find the percentage
61
188
61 ÷ 188 ≈ 0.32
32%
3) Compare both samples by
finding the mean
24% and 32%
24 + 32 56
≈ 28%
≈
2
2
4) Round (make the number
end with a zero or a 5)
About 30% of the barrel is
green
EXAMPLE #2
In each situation, would it make more sense to
study the entire population or a sample?

David got a new shipment of dog treats. Each
small bag is supposed to contain pieces of real
beef jerky. David wants to know the mean
number of pieces of beef jerky per bag.
the
or
It would take too long to count jerky in all
bags, so it’s best to take a sample from one
two bags.
EXAMPLE #3
Kristen wants to know the mean height of her cat’s
new kittens.

A cat can only have so many kittens. It won’t be
terribly difficult measuring a few cats that live in
the house, so you can study the entire population.
EXAMPLE #4
Dog Owners
Breed
Percent
Beagle
35%
German Shepherd
30%
Retriever
25%
Other
10%
The table shows the results of a poll in 1999 of 500 dog owners in
a large city. Were the statistics drawn from a sample or from the
entire population?
The population is all the dog owners in the city. Is it
possible to poll every single owner?
No, it even tells you that only 500 dog owners were polled.
3-6 SAMPLING METHODS
IWBAT understand how the method of sampling
determines how representative the sample is of
the population.
VOCABULARY
Biased – A sample that does not mirror the
population.
 Random Sampling – A sample where each person
or thing has an equal chance of being chosen.
 Representative – A sample that mirrors the
population.
 Convenience Sampling – Any convenient method
to use to choose the sample.
 Responses to a Survey – A form of sampling
where you ask people to take a survey. Tends to
be biased since those with strong opinions are
more likely to take a survey.

EXAMPLE #1

Cassie wants to determine which brand of athletic
shoes is most popular with U.S. middle school
students. She decides to stand near the entrance of
the school and keep a count of what brands of shoes
students are wearing when entering the school.
1.
What sampling method is Cassie using? How do you
know?
Convenience Sampling because she’s going to
her own school.
2.
Is it likely to be representative or biased? Explain.
Biased because she is only studying the students
at her school and not at any other schools.
MORE EXAMPLES
Tell whether each sample is likely to be representative or
biased. Explain your answers. Identify each as random
sampling, convenience sampling, or responses to a survey.
1.
A state legislator mails questionnaires about literacy to
all the eligible voters in her district. Only 12% of the
people return the questionnaire.
Biased because people who are illiterate won’t be able
to read the questionnaire.
This is responses to a survey.
2.
A school principal questions every student whose locker
number ends in a 9 to gather student input about plans
for the new library.
Representative because students of different grade
levels and interests would be studied.
This is random sampling.
3-7 MAKE A GRAPH
IWBAT make graphs to illustrate data and solve
problems.
3-8 ANALYZING STATISTICAL
RESULTS
IWBAT evaluate the effect of questions on
statistical results.
3-9 REPRESENTING A POINT OF
VIEW
IWBAT analyze data displays and evaluate the
influence of the display on the conclusions.

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