This document discusses measures of central tendency including the mean, median, and mode. It provides examples to calculate and compare the mean, median, and mode for sets of data. The mean is the average value, the median is the middle value, and the mode is the most frequent value. The document explains that the mean may be higher or lower than the median depending on whether there are more values above or below it. It also gives an example of calculating the mean, median, and mode for golf scores to determine which player has the better average score.

1. Central Tendencies
Mean Median, Mode
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2. The mean is the average value of all the data in the set.
The median is the value that has exactly half the data above it
and half below it.
The mode is the value that occurs most frequently in the set
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3. A Math Song
Mean, median, mode
Mean, median, mode
Central tendency
Central tendency
The mean is the average of what you’ve got
The median’s the one in the middle spot
The mode is most frequent of the lot
The mean, median , mode
Mean, median, mode
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4. Example 1
Mark Fehr received the following marks on nine mathematics tests:
{80, 74, 72, 71, 25, 68, 71, 50, 80}
1. Calculate the median of these marks.
2. How many marks are less than the median? How many marks
are greater than the median?
3. Calculate the mean of these marks.
4. How many marks are less than the mean? How many marks
are greater than the mean?
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5. Conclusion
* The median mark is the middle mark. By definition, there are as
many values below the median as there are above the median.
* The mean is not the middle mark. There are more marks above
the mean than below it.
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6. Consider the golf scores of two players who play nine holes
of golf. Note that Player #1 was stuck in a sand trap on the
ninth hole.
1. Calculate the mean, median, and mode of the scores of
Player 1
2. Calculate the mean, median, and mode of the scores of
Player 2
3. In your opinion, which player has the better average score
per hole? Explain.
4. In your opinion, which measure of central tendency is the
most appropriate to use in this situation?
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7. Create a list of five numbers from 0 to 10 having the following characteristics:
* mean = 6
* median = 6
* mode = 3
* no number can appear more than twice
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8. Solution
Since the median is six, choose six for the middle number.
__, __, 6, __, __
Since the mode is three, choose the lowest two numbers to be three.
3, 3, 6, __, __
In order that the list of five numbers has a mean of six, the sum of the numbers must be:
= 5 x 6
= 30
The sum of the first three numbers is:
= 3 + 3 + 6
= 12
The sum of the remaining two numbers is:
= 30 – 12
= 18
Since the remaining numbers have to be different from each other (they cannot form a
mode), and less than or equal to 10, choose 8 and 10.
Therefore, the numbers are: {3, 3, 6, 8, 10}
Mean: 30 ÷ 5 = 6
Median: 6
Mode: 3
No number appears more than twice.
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