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.

**Related Pages**

Center Of A Distribution

Median

Mode

Central Tendency

More Statistics Lessons

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?**

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:**

- 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?
- 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?
- 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?

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