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Math
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The term "measures of central tendency" is a
fancy name for mean, median and mode.
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Mean: |
Average.
The sum of a set of data divided by the
number of data. (Do not round your answer
unless directed to do so.) |
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Median: |
The middle value or the mean of the
middle two values, when the data is
arranged in numerical order.
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Mode: |
The value ( number) that appears the
most.
It is possible to have more than one mode,
and it is possible to have no mode. If
there is no mode-write "no mode" , do
not write zero (0) . |
Always check your work with a calculator!!
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How to use
your
TI-83+ graphing calculator with
mean, mode, median.
Click calculator. |
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Example #1
Find the mean, median and mode for the following data:
5, 15, 10, 15, 5, 10, 10, 20, 25, 15. You
need to organize
the data.
|
number |
tally |
frequency |
|
5 |
// |
2 |
| 10 |
/// |
3 |
| 15 |
/// |
3 |
| 20 |
/ |
1 |
| 25 |
/ |
1 |
(A tally/frequency table is one way to organize data.)
Mean
sum of the data
130 = 13
number of data 10
Median 5, 5, 10, 10,
10, 15, 15, 15, 20, 25
I have found that listing the data out in order is the easiest way to find the median. The numbers
10 and 15 both fall in the middle. I have to average these two numbers to get the median.
10 + 15 = 12.5
2
Mode Two numbers appear the most
often: 10 and 15.
The table shows there are three 10's and three
15's. In this example there are two answers
for the mode. |
APPLICATIONS
Example #2
For what value of x will 8 and x have the same mean (average) as 27 and 5?
27 + 5 = 16
2 |
x + 8 = 16
cross multiply
2
and solve
32 = x + 8
-8
- 8
24 = x |
Example #3 :
Part II question
On his first 5 biology tests, Bob received the following scores: 72, 86, 92, 63, and
77. What test score must Bob earn on his sixth test so that his average (mean score) for all six tests will be 80?
Show how you arrived at your answer. [3]
Possible solution:
72 + 86 + 92 + 63 + 77 + x
= 80
6
cross multiply
(80)(6) = 390 + x
480 = 390 + x
- 390 -390
90 = x
Example #4
Part III question
The mean (average) weight of three dogs is 38 pounds. One of the dogs, Sparky, weighs 46 pounds. The other two dogs, Eddie and Sandy, have the same weight. Find Eddie's weight.
Let x = Eddie's weight
( they weigh the same so
Let x = Sandy's weight
they are both "x")
Average: sum of the data divided by the number of data.
x + x + 46 = 38
cross multiply and
3(dogs)
solve
(38)(3) = 2x + 46
114 = 2x + 46
-46 -46
68 = 2x
2 2
34 = x Eddie weighs 34 pounds.
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