ACT Math - How to find arithmetic mean

Angela scores 17, 19, 13, 24, and 14 points in the first five games of a seven-game basketball season. If the scoring leader in Angela’s league averages 18 points per game, how many points must Angela score in the final two games combined to end the season with the highest scoring average in the league AND have a higher scoring average than any other player?

Explanation

Since a given player’s scoring average can be determined by dividing the sum total of points scored by the number of games, we can determine the total points of the scoring leader by multiplying the average points per game by the total number of games. 18 x 7 = 126. Angela would have to score 1 more point than the current scoring leader. Angela’s current total is 87 points; therefore, she must score 40 (87 + 40 = 127) over the course of the final two games to have the highest average points per game in the league.

Find the arithmetic mean of this set of data:

{0, 0, 0, 0, 1, 5}

Explanation

The sum of all the terms is 6. The number of terms in the set is 6. 6/6 = 1

Greg got an average of 93 on his test scores this semester. He got a 92, 93, and 97 on the first three tests. If he received the same score on each of his last three tests, what was his score on each of these tests?

92.33

90.5

Explanation

We can set up an equation (92 + 93 + 97 + 3x)/6 = 93. Solving for x yields 92.

Bryan earned $8/hr working a 6-hour shift each day, Tuesday thru Thursday, at his job as a server. He also earned $7.75/hr tutoring for a 2-hour shift each day, Friday thru Sunday. What were his daily average earnings for the 6 day period?

$30.75

$31

$31.75

$32

$35

Explanation

We multiply the $8 by the 6 hours, and by the three 3 days that Bryan worked at his job as a server. 8 * 6 * 3 = 144

We then multiply the $7.75 an hour, by the 2 hour shift and by 3 days to get the total Bryan earned at his tutoring job. 7.75 * 2 * 3 = 46.50

We then add the totals: 144 + 46.50 = 190.50

Then divide by 6 days, getting an average of $31.75 per day.

Mark has a job mowing lawns for some of the people in his neighborhood. If Mark gets paid $30 per lawn, and it takes him 40 minutes to mow a lawn, what is his average hourly pay if he typically spends 4 hours total mowing lawns?

$25/hr

$30/hr

$35/hr

$40/hr

$45/hr

Explanation

This question requires us to do a few things. First, we must figure out how many lawns Mark mows in 4 hours.

4 hours x 60 minutes/hr = 240 minutes.

240 minutes ÷ 40 minutes/lawn = 6 lawns.

6 lawns x $30/lawn = $180

So, he made $180 in a matter of 4 hours.

$180 ÷ 4 hours = $45/hr

The mean of five numbers is 40. The mean of the smallest two numbers is 25. What is the mean of the other three numbers?

Explanation

The equation for the mean of a group of numbers is to find the sum of all of the numbers and then divide by how many numbers are in the group. This means that if we know the mean and how many numbers are in the group, we can find the sum of those numbers.

(sum of all five numbers) / 5 = 40 --> sum of all five numbers = 200

(sum of two smallest numbers) / 2 = 25 --> sum of two smallest numbers = 50

Subtracting the sum of the two smallest numbers from the sum of all five gives us the sum of the remaining three. We can then divide by three to find the mean of those three remaining numbers.

200 – 50 = 150

150 / 3 = 50

Ashley scored 80, 80, 83, 85, 90, and 77 on her tests this semester. If she wants an average of 85 on all her tests, which would she have to score on her final test?

100

None of the other answers.

Explanation

One can set up an equation for the average test score. 85=(80+80+83+85+90+77+x)/7.

Solving for x gives 100.

Jenny just got her spring report card. She earned 3 As, 2 Bs and one C. If the values assigned to grades are 4 points for an A, 3 points for a B, and 2 points for a C, what is her GPA, rounded to the nearest tenth?

3.3

3.0

3.1

3.7

3.5

Explanation

GPA is the average of the grade points.

GPA = (3*4 + 2*3 + 1*2) / 6 = 3.33

If the average of A, B, and C is 50, which of the following expressions represents the average of A, B, C, and D?

(150 + D) / 4

(50 + D) / 4

(150 + D) / 3

\[150 - (A + B + C)\] / 4

Explanation

We take the average 50 and multiply it by 3 (the number of terms in the set) to get the total sum of the initial set. Then you take the total sum and add D and divide by the numbers of terms in the new set.

If Point $X$ is located at $-10$ on a number line and Point $Z$ is located at $101$ on the same line. What is the midpoint of line $XZ$ ?