Math Statistics: Mean

The mean of a set of observations is the average. It is obtained by dividing the sum of data by the number of observations.

The formula is:

Example:

Find the mean of the following set of integers.

8, 11, –6, 22, –3

Solution:

Example:

The set of scores 12, 5, 7, -8, x, 10 has a mean of 5. Find the value of x.

Solution:

Problems Involving Mean

When there are changes in the number or the values of the observations in a set, the mean will be changed.

Example:

The mean score of a group of 20 students is 65. Two other students whose scores are 89 and 85 were added to the group. What is the new mean of the group of students?

Solution:

The formula:

can rewritten as:

Total score = Mean × Number of students

Total score of the original group = 65 × 20 = 1,300

Total score of the new group

= Total score of the original group + scores of the 2 new students

= 1,300 + 89 + 85 = 1,474

Number of students in the new group

= Number of students in the original group + Number of new data

= 20 + 2 = 22

Example:

The mean of a list of 6 numbers is 20. If we remove one of the numbers, the mean of the remaining numbers is 15. What is the number that was removed?

Solution:

Using the formula: Sum = Mean × Number of numbers

Sum of original 6 numbers = 20 × 6 = 120

Sum of remaining 5 numbers = 15 × 5 = 75

Number removed = sum of original 6 numbers – sum of remaining 5 numbers

=120 – 75 = 45

Alternative Method:

Let x be the removed number

The removed number is 45

Example:

10 students of a class had a mean score of 70. The remaining 15 students of the class had mean score of 80. What is the mean score of the entire class?

Solution:

Total score of first 10 students = 10 × 70 = 700

Total score of remaining 15 students = 15 × 80 = 1200

Mean score of whole class

The following video shows you how to find the mean or average of a set of numbers.

The following video shows how to calculate the mean, median, mode and range of given data sets.

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