Math Study Guide: Topic 7: Averages (pages 37-40)

Question 1

What is the “average” of a group of numbers?

(and what is another word for “average?”)

Answer 1

The “average” of a group of numbers is simply the sum of the numbers divided by the number of terms.

(and “mean” is another word for “average”)

Question 2

How do you solve the following?

What is the average of 12, 15, 2, and 11?

Answer 2

Just add the four numbers (12 + 15 + 2 + 11 =40

Then divide by the number of terms (4):

40 ÷ 4 = 10

Question 3

How do you solve the average of numbers which are equally spaced?

Answer 3

Arrange the numbers in increasing order, and then identify the number that is in the middle.

• Example:* What is the average of 320, 322, 324, 326, and 328? (324)
• Example:* What is the average of 320, 322, 324, 326, 328, and 330? (325)

Question 4

What is the easiest way to solve the following?

There are 52 cars, which weigh 4,000 pounds each, and 26 trucks, which weigh 10,000 pounds each. What is the average weight of all the vehicles?

Answer 4

Put 52 over 26, which equals a ratio of cars to trucks of 2:1

So, solve as if there are only 2 cars and 1 truck =

(2 x 4,000 + 1 x 10,000) ÷ 3 = 18,000 ÷ 3 = 6,000

Question 5

How would you solve the following?

The average of Mary’s four test scores is 88. If her lowest test score was dropped, the average of the remaining test scores is 92. What was her lowest test score?

Answer 5

Multiply the average times the number of terms to get the total.

Multiply 88 x 4 (to get the total of Mary’s tests)
Then multiply 92 x 3 (to get the total of her three highest scores)

Then subtract the two totals to get her lowest score:

352 - 276 = 76