# Math Statistics: Mean

In these lessons, we will learn how to calculate the mean of a given data set. We will also learn how to solve word problems involving 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: How to calculate the mean, median, and mode and range of a given data set?

### Word 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

Number removed = 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 Mean Word Problems

Example 1:
Pedro’s luncheonette is open six days a week. His income for the first five days was \$1,200, \$1,100, \$2,000, \$1,400 and \$3,000. How much money must she make on the sixth day to average \$2,000 for the six days?

Example 2:
George’s scores on three math tests were 70, 90 and 75. What score does he need on the fourth test to have a final average of 80?

How To Solve Word Problems With Averages?

Examples:

1. Timothy’s average score on the first four tests was 76. On his next five tests his average score was 85. What was his average score on all nine tests?
2. Tracy mowed lawns for two hours and earned \$7.40 an hour. Then she washed windows for three hours at \$6.50 per hour. What was Tracy’s average earnings per hour for all five hours?
3. After taking three quizzes, your average is 72 out of 100. What must your average be for the next five quizzes to increase your average to 77?

Solving Average Word Problems

Example:
On her first four games, Jennifer bowled 101, 112, 126, 108. What is the minimum score she must bowl in her fifth game in order to have an average of 110?

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations. 