ACT Math : Data Analysis
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Example Questions
Example Question #21 : Arithmetic Mean
On the last Algebra exam, Sarah scored 87, Amy scored 63, and Jessica scored lower than Sarah but higher than Amy. What is Jessica's score if the mean of their three scores is 52 points higher than the range of their scores?
The range of a set of data is the difference between the highest and lowest values in the set. Since Jessica scored between Sarah and Amy, the range must be the difference between Sarah and Amy's scores.
If the mean is 52 points higher than the range, the mean must be 
The mean is the sum of the values in the set divided by the number of values in the set.
Let Jessica's score be denoted by 
Solve for 
Example Question #28 : Arithmetic Mean
Last week, gas sold in the 92 gas stations in Jonestown for an average of $3.32 per gallon, and gas sold for an average of $3.42 per gallon in the 142 gas stations in Smithsville. What was the average price of gas per gallon in all of the gas stations of Jonestown and Smithsville together?
Assume that the price of gas in every gas station of each town is exactly the average price. The equation you would write would then be as follows:
The correct answer is $3.38 per gallon.
Example Question #21 : Arithmetic Mean
Susan checked her grades and saw that she had averaged an 88% on the last four tests. After taking the fifth test, her average grade was now 90%. What grade did she get on her fifth test?
Because her average grade after 5 tests was 90% and the first four tests averaged 88%, write the following expression:
Example Question #30 : Arithmetic Mean
What is the sum of the range, mean, mode and median of the following data set:
Arrange the data set from smallest to largest:
Range: 
Median: number in the middle, or
Mode: number most often repeated, or
Mean: the sum of all numbers divided by the total number of data points, or
The sum of all these measures is 
Example Question #31 : Arithmetic Mean
Fred received an 82, 85, and 95 on his first 3 tests of the semester. All tests are out of 100 points. What must Fred score on the fourth and final test to have an average of 90 for the class?
The answer is
The total points for the four tests are 
This simplifies to 
Subtract 262 from both sides to determine that 
Example Question #32 : Arithmetic Mean
If Jamison scored a 68, 88, 82, and 56 on each of his exams, what score must he get on his final test, weighted equally, to recieve a passing average 
This question at first may seem like a daunting amount of arithmetic, but it should be an easy question or essentially free points on the ACT. The problem is set up as a simple equation of averages, shown by:
Where 
After adding each of the four tests together, we have:
Multiple both sides by 5,
Then solve for 
Do not be intimidated by questions like these, they are straight-forward and only involve arithmetic.
Example Question #31 : Arithmetic Mean
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) / 3
(50 + D) / 4
(150 + D) / 4
[150 - (A + B + C)] / 4
(150 + D) / 4
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.
Example Question #34 : Arithmetic Mean
Calculate the arithmetic mean of the following set of numbers: 54, 35, 50, 49, 54, 65, 82, 54, and 25.
54
53
52
51
52
To solve this question, you must know that the mean is the sum of the values divided by the number of values, in this case: 468/9=52. It is not 54, which is the median (the most commonly occurring number of the set).
Example Question #31 : Arithmetic Mean
In a theatre there are 600 people. Out of this, 100 males have an average age of 50 and 500 females have an average age of 30. To the nearest whole year, what is the average age of the town’s entire population?
34
43
32
33
40
33
To find the average age, compute:
100 * 50 + 500 * 30= 5000+ 15000= 20000. Then divide by the total amount of people that are at the theatre: 20000/600= 33.3=33.
Example Question #31 : Arithmetic Mean
Jack earned $10 on Tuesday. On each following day, through Satuday, he earned $3 more than the preceding day. What were his mean earnings for the five-day period, Tuesday through Saturday?
$16
$80
$15
$5
$50
$16
Jack earned $10 on Tuesday, $13 on Wednesday, $16 on Thursday, $19 on Friday, and $22 on Saturday. This is a total of $80. Divide that by the total number of days, 5, and the mean is $16.
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