ACT Math : Data Analysis
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Example Questions
Example Question #11 : Arithmetic Mean
Find the arithmetic mean of the given set of numbers:
{0,12,10,8,15,5,20}
12
11
8.33
7
10
10
The sum of this set of numbers is 70. There are 7 elements in the set, so 70/7 = 10 which is your mean.
Example Question #31 : Data Analysis
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?
$31.75
$31
$35
$32
$30.75
$31.75
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.
Example Question #31 : Data Analysis
History class has three major exams that make up Joe’s grade. If he scores an 88 on the first exam, an 86 on the second exam and a 96 on the third exam, what is his average grade on all three exams?
90
88
92
96
86
90
Average or Mean = Sum of the Options / # of Options
Average = (88 + 86 + 96) / 3 = 270/3 = 90
Example Question #32 : Data Analysis
Find the mean: 8, 11, 17, 17, 18, 19, 22
Finding the mean is the same thing as finding the average. First add all the integers together which yields 112. Then divide the sum by the number of integers, 6.
Example Question #2741 : Act Math
The average of four numbers is 27. A new number, 
The value of 
Example Question #33 : Data Analysis
Jameson received four grades on his algebra tests, which brought his average to an 88. What grade would he have to make on his final test in order to bring his average up to a 90?
To start, we have to understand the concept behind averages. To average something, take all your numbers, add them together and then divide by the total amount of numbers. Also, the definition of an average is a quantity intermediate to a set of quantities, or in other words, the exact middle.
In this particular problem, we know that the average of the first four tests is an 88, which means that the summation of the first four tests divided by 4 must equal 88. We can extrapolate from the definition of an average that the first four tests can all be estimated at 88.
When adding in the fifth test, we must then account for 5 tests as opposed to 4. We can set up and solve the formula for the fifth test's grade as such:
(
Multiply both sides by 5.
Jameson must score a 98 on his last test to bring his average up to a 90.
Example Question #22 : Arithmetic Mean
If Point 
The line is 111 points long, meaning the midpoint is 55.5 away from either end. Simply subtract 55.5 from 101 to yield 45.5.
Example Question #23 : Arithmetic Mean
Brenda's cat gave birth to 6 kittens. The kittens weights are listed below.
What is the average weight of one of Brenda's kittens?
Sum of the weights divided by 6.
Example Question #34 : Data Analysis
A graduating class has 300 women and 250 men. The women's ages average to 27 and the men's ages average to 29. What is the average age of the class?
Example Question #25 : Arithmetic Mean
In Town A, the average price of gas at all 45 gas stations is $3.31 per gallon. In Town B, the average price of gas at all 20 gas stations is $3.22 per gallon. What is the average combined average price of gas in both towns?
Assume that all gas stations in Town A are selling the gas at $3.31 per gallon and all gas stations in Town B are selling the gas at $3.22 per gallon. To find the average price per gallon across all stores, you write the following formula:
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