Mean (Average)

Mean (Average)

How to find the mean (average) of the given data: formula, examples, and their solutions.

Formula

(mean) = (sum)/n. (mean): Average, Specifically the arithmetic mean, (sum): Sum of the data, n: Total number of the data

(mean) = (sum)/n

(mean): Average, Specifically the arithmetic mean
(sum): Sum of the data
n: Total number of the data

The mean is one of the ways
to represent the whole data.

The other ways to represent the whole data
are the median and the mode.

Median

Mode

Example 1

Find the mean of the given test scores. 60, 70, 80, 90, 100

The sum of the test scores, (sum), is
60 + 70 + 80 + 90 + 100.

60 + 100 = 160
70 + 90 = 160

160 + 160 = 320

320 + 80 = 400

So the sum is 400.

The number of the test scores, n, is 5.

(sum) = 400
n = 5

So (mean) = 400/5.

400/5 = 80

So 80 is the answer.

This means
the mean 80 represents
the given data {60, 70, 80, 90, 100}.

Example 2: Mean from the Frequency Table

Find the mean of the given data.

To find the mean from the frequency table,

make a column for (Scores)⋅(Frequency)
right next to the given table.

By using this column,
you can find the sum of the given data.

Write (Score)⋅(Frequency) column
by multiplying (Scores) and (Frequency).

0⋅1 = 0
1⋅1 = 1
2⋅4 = 8
3⋅7 = 21
4⋅5 = 20
5⋅2 = 10

Use (Scores)⋅(Frequency) column
to find the sum of the data.

(sum) = 0 + 1 + 8 + 21 + 20 + 10
= 60

Use the Frequency column
to find n: the number of the data.

n = 1 + 1 + 4 + 7 + 5 + 2
= 20

(sum) = 60
n = 20

So (mean) = 60/20.

60/20 = 3

So 3 is the answer.