Download Mean, Median and Mode

Mean, Median, and Mode
~Central Tendency~
Lesson 1-9
Mrs. Robertson
Mean?
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Mean: the sum of the data items divided
by the number of data items.
These are data items:
2, 3, 4, 5, 8, 8, and 12
2 + 3 + 4 + 5 + 8 + 8 + 12
7 (total data items)
42 / 7 = the mean, which is 6
Median?
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Odd Number of Data Items: the middle
number when the data items are put in
numerical order.
Even Number of Data Items: the two
middle numbers when data items are put
in numerical order.
Median is the middle of the road
Median?
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So find the median with these data items.
2, 3, 4, 5, 8, 8, and 12
They’re in order
There are 7 numbers, meaning odd.
So which is the middle most number?
The median is 5.
Mode?
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Mode: is the data item that occurs most
often.
There can be one mode, multiple modes,
or no mode. You can say how many
modes there are too!
What about our previous data set?
2, 3, 4, 5, 8, 8, and 12
8 is a mode for these data items.
Find me the M, M & Ms
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12, 14, 26, 37, 8, and 14
Re-order: 8, 12, 14, 14, 26, 37.
Mean: 18.5
Median: 14
How many Modes: 1
Mode: 14
Find me the M, M & Ms
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2.3, 4.3, 3.2, 2.9, 2.7, and 2.3.
Re-order: 2.3, 2.3, 2.7, 2.9, 3.2, 4.3.
Mean: 2.95
Median: 2.8
How many Modes? 1
Mode: 2.3
Find me ONLY Mode:
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Grape, grape, banana, nectarine,
strawberry, strawberry, strawberry,
orange, watermelon.
How many modes?
Just one: strawberry.
How many modes?
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11, 9, 7, 7, 8, 8, 13, 11
3 Modes
38.5, 55.4, 45.3, 38.5, 68.4
1 Mode
Outlier
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Outlier: is a data item (data value) that is
much higher or lower than the other data
values.
Outliers can affect the mean of a group of
data.
Example: 2, 3.5, 1, 2.5, 5 billion.
Example: 35, 45, 40, 37, -6.
Describing Data with M, M, & M.
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You can use what you know about Mean,
Median, and Mode to describe data.
But figuring out which M describes it best
is difficult.
Nah! Its got to
be mean!
I think mode
describes it best!
Which M, M, & M is best?
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The favorite movie of students in the
eighth grade class?
Mode: good for non-numerical data items
and for frequent occurrences.
Which M, M, & M is best?
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The distances students in your class travel
to school.
Median: one student may live much further
than everyone else. When an outlier may
significantly influence the mean, we use
median.
Which M, M, & M is best?
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The daily high temperature during a week
in July.
Mean: since daily temp. are not likely to
have outlier, mean is best. When data
have no outlier, use mean.
Measures and Central Tendency
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Your text book is going to ask you
determine which MEASURE of CENTRAL
TENDENCY best describe the data.
Its just asking you to figure out which M
works with the data best!
Using Formulas
Section 3.4
Just two formulas.
Substituting into Formulas
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Formula is an equation that shows a
relationship between quantities that are
represented by variables.
Like: Susie has b books. b is the number
of books Susie has. b stands for
something.
Rate
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Distance = rate • (time)
d = rt
Cause remember? r and t next to each
other means you multiply them.
So…rate multiplied by time = distance.
Obvious Example: d = r • t
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Suppose Ms. Dewey-Hoffman traveled
162 miles in 2 hours. Use the formula.
How fast was I going? What was my rate?
d=r•t
d = distance, or 162 miles.
t = time, or 2 hours.
162 miles = r • 2 hours.
Obvious Example: d = r • t
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Suppose Ms. Dewey-Hoffman traveled 162
miles in 2 hours. Use the formula.
What was my rate?
162 miles = r • 2 hours.
2 hours
2 hours
162  2 = 82 miles/hour
So, Ms. Dewey-Hoffman was traveling at 82 miles/hour
to go 162 miles in 2 hours. 82 mph is my r or rate. =]
Try These: d = r • t
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d = 200 yards, t = 24 seconds
What don’t we know? Set up equation.
Solve.
r = 30 feet/minute, t = 5 minutes
What don’t we know? Set up equation.
Solve.
Perimeter Formula: P = 2l + 2w.
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Perimeter = 2(length) + 2(width).
L
• The formula simplifies how the
perimeter of a rectangle works.
W
W
• Perimeter = l + l + w + w…so…
• Perimeter = 2l + 2w
L
Try These: Tell Me Perimeter
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Remember: P = 2l + 2w
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Length = 16.8cm, Width = 27.3cm
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Length = 8.6cm, Width = 17.4cm
W
L
Assignment #16
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Pages: 134-135: # 5-8 All, 15-18 All.
Pages: 139-140: # 5–21 Odd.
Make sure you answer ALL parts of each
problem, the first set of problems ask for a
lot.