Math Statistics: Mean

In this lesson, we will learn how to find the mean of a given data set. We will also learn how to solve word problems involving mean.

Related Topics: More Lessons on Statistics

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:

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.
Find the mean, median, mode and range of the data 15, 24, 49, 8, 50



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

=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
1. Pedro's luncheonette is open six days a week. His income for the first five days was $1,200, $1,200, $2,000, $1,400 and $3,000. How much money must she make on the sixth day to avaerage $2,000 for the six days?
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.
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 wahed 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 quizzesto increase your average to 77?



Solving Average Word Problems
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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