3.3 Mean, Median, Mode, Formulas

Review of Mean, Median, and Mode, as well as the Rate Formula and Perimeter Formula.

1. Remember the 3 Ms?
Mean, Median, and Mode
~Central Tendency~
Section 3.3
September 30, 2008
By Ms. D-H

2. Mean?
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

3. Median?
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

4. Median?
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.

5. Mode?
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.

6. Find me the M, M & Ms
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

7. Find me the M, M & Ms
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

8. Find me ONLY Mode:
Grape, grape, banana, nectarine,
strawberry, strawberry, strawberry,
orange, watermelon.
How many modes?
Just one: strawberry.

9. How many modes?
11, 9, 7, 7, 8, 8, 13, 11
3 Modes
38.5, 55.4, 45.3, 38.5, 68.4
1 Mode

10. Outlier
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.

11. Describing Data with M, M, & M.
You can use what you know about Mean,
Median, and Mode to describe data.
But figuring out which M describes it best
is difficult.
I think mode
describes it best!
Nah! Its got to be
mean!

12. Which M, M, & M is best?
The favorite movie of students in the
eighth grade class?
Mode: good for non-numerical data items
and for frequent occurrences.

13. Which M, M, & M is best?
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.

14. Which M, M, & M is best?
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.

15. Measures and Central Tendency
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!

16. Using Formulas
Section 3.4
Just two formulas.

17. Substituting into Formulas
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.

18. Rate
Distance = rate • (time)
d = rt
Cause remember? r and t next to each
other means you multiply them.
So…rate multiplied by time = distance.

19. Obvious Example: d = r • t
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.

20. Obvious Example: d = r • t
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. =]

21. Try These: d = r • t
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.

22. Perimeter Formula: P = 2l + 2w.
Perimeter = 2(length) + 2(width).
W W
L
L
• The formula simplifies how the
perimeter of a rectangle works.
• Perimeter = l + l + w + w…so…
• Perimeter = 2l + 2w

23. Try These: Tell Me Perimeter
Remember: P = 2l + 2w
Length = 16.8cm, Width = 27.3cm
Length = 8.6cm, Width = 17.4cm
W
L

24. Assignment #16
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.