Mean, Mode

AVERAGES (MEAN, MEDIAN, AND MODE)

INSTRUCTION SHEET

A. Finding the Mean

The mean of a set of values is the sum of the values divided by the number of values. It is also called the average.

Example: Find the mean of 19, 13, 15, 25, and 18

19 + 13 + 15 + 25 + 18 = 90 = 18

5 5

When the mean is known and you must find a missing value, some simple rules of algebra must be applied.

Example: Cory has received the following grades this term: 75, 87, 90, 88, 79. If he wishes to earn an 85 average, what must he score on his final test?

Set up the problem like this: 75 + 87 + 90 + 88 + 79 + s = 85

6

To solve:

1. Add the known values.

419 + s = 85

6

2. Next, we want to try to isolate the unknown (s) on one side of the equation. To do this we must use inverse operations to eliminate the numbers on the side of the equation with the unknown (this means we do the opposite of what is being done).

Start with the 6. Since we are dividing the expression 419 + s by the 6, we must now multiply it by 6. NOTE: Whatever you do to one side of the equation, you must do to the other side of the equation as well. Therefore, I will multiply the 85 by 6 too.

6 x 419 + s = 85 x 6

6

I can cancel the 6s on the left side of the equation. This leaves you with the equation:

419 + s = 510

Now we must eliminate the 419 from the side of the equation with the unknown. Since we are adding 419 to s, we will subtract it from both sides of the equation.

419 + s = 510 – 419

- 419

0

This leaves us with: s = 91

Answer: The student will need to score a 91 on his last test to earn an average of 85 for the term.

B. Finding the Median

The median refers to the midpoint in a series of numbers.

To find the median, arrange the numbers in order from smallest to largest. If there is an odd number of values, the middle value is the median. If there is an even number of values, the average of the two middle values is the median.

Example #1: Find the median of 19, 29, 36, 15, and 20

In order: 15, 19, 20, 29, 36 since there are 5 values (odd number), 20 is the

median (middle number)

Example #2: Find the median of 67, 28, 92, 37, 81, 75

In order: 28, 37, 67, 75, 81, 92 since there are 6 values (even number), we

must average those two middle numbers to get the median value

Average:

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