ACT Math : Data Analysis
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Example Questions
Example Question #33 : Arithmetic Mean
Fred has had three algebra tests so far and has one left before he gets a final grade. He wants an "A" in the class, and so he needs at least a 90% average test grade to get an "A". His previous test scores have been 96%, 86%, and 94%. What is the lowest score he can get on his fourth test to get an "A" in the class?
94%
84%
88%
90%
85%
84%
The following equation can be set up in order to solve for the score on the fourth test, x. The left side of the equation is the average of all of his tests. This is then set equal to 90%, the average test score which guarantees him an A: (96+86+94+x) / 4 = 90. Solving for x, we get x = 84%.
Example Question #34 : Arithmetic Mean
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?
$45/hr
$25/hr
$40/hr
$30/hr
$35/hr
$45/hr
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
Example Question #37 : Arithmetic Mean
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
3.1
3.5
3.0
3.7
3.3
GPA is the average of the grade points.
GPA = (3*4 + 2*3 + 1*2) / 6 = 3.33
Example Question #32 : Arithmetic Mean
A student has scored 93, 87, and 94 on three of his four exams. In order to maintain a 90 average or above in the class, what is the lowest this student may score on the fourth exam?
78
92
88
89
86
86
In order to have an average of 90 over four exams, that means the sum of all the students scores must total to at least 360.
So far, the student has a total sum of 274 points.
360 - 274 yields 86, the minimum score needed to maintain an average of 90 or higher
Example Question #41 : How To Find Arithmetic Mean
A thermometer reads an average of 47.5 °F on a Sunday, rises 2.9 degrees on Monday, and drops 1.7 degrees on Tuesday. What is the average reading of the thermometer on Tuesday?
Use 47.5 as a baseline value to add and subtract the subsequent drops on Monday and Tuesday. Thus, 47.5 + 2.9 = 50.4 (Monday); 50.4 - 1.7 = 48.7 (Tuesday).
Example Question #42 : Statistics
What is the sum of the mean and the median of the following set of numbers:
5, 12, 7, 28, 8?
None of the answers are correct
8
24
12
20
20
First, put the data in ascending order: 5, 7, 8, 12, 28
Mean = average = (5 + 7 + 8 + 12 + 28) ÷ 5 = 60 ÷ 5 = 12
Median = middle number = 8
Mean + Median = 12 + 8 = 20
Example Question #43 : Statistics
Samantha’s semester math grade is based on the average of five unit tests. She has already achieved test scores of 88, 92, 79, and 95. What does she need to score on her next test to obtain a 90 as the final grade for the semester?
85
None of the answers are correct
89
90
96
96
To get an average of 90 for the five tests, she must score a total of 450 points (90 x 5). If you add up the first four test scores, the total is 354 points (88 + 92 + 79 + 95). Subtracting where she is from where she wants to be (450 – 354), you get a fifth test score of 96.
Example Question #42 : Arithmetic Mean
Jill has received $200 on her birthday each year for four consecutive years. For the next two years she received $700 in total. For this 6-year period, what was her average yearly amount of birthday money she received?
$350
$275
$200
$400
$250
$250
We add $200 times the four years, giving us $800. We then add $700 for the following two years, giving a total of $1,500. We divide this by 6 years, giving us an average of $250 per year.
Example Question #42 : How To Find Arithmetic Mean
Find the arithmetic mean of the following set of data:
{1,2,3,4,6,8}
The total sum of the elements of the set is 24. There are 6 terms in the set.
24/6 = 4
Example Question #44 : Arithmetic Mean
The following are the points scored on a test by students in a class:
5,9,11,12,13,13,18,20
Which of the following is closest to the mean?
15
13
12
11
14
13
13 is the correct answer. The mean is all the scores divided by the number of scores, which in this case is 12.625.
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