SAT Math : Data Analysis
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Example Questions
Example Question #22 : How To Find Arithmetic Mean
The median of a set of ten consecutive integers is –2.5. What is the mean of this set?
–2.5
2.5
0
2
–1
–2.5
Let's let a, b, c, d, e, f, g, h, i, and j represent the integers in the set from least to greatest.
The set has an even number of integers. This means that the median will have to be the average of the two numbers in the middle. The middle numbers will have to be the fifth and the sixth numbers, which are represented by e and f. This means that the average of e and f must be –2.5. Because –2.5 is halfway between –3 and –2, this means e is –3 and f is –2. Our set looks like this so far:
a, b, c, d, -3, -2, g, h, i, j
Because the set consists of consecutive integers, each term must equal one more than the one before it. So, g, h, i, and j are the four numbers are –2, and a, b, c, and d are the four numbers before –3. Thus, our set is as follows:
–7, –6, –5, –4, –3, –2, –1, 0, 1, 2
The question asks us to find the mean, which is the sum of the elements in the set divided by the number of elements in the set.
The sum of the numbers in the set is –7 + –6 + –5 + . . . 1 + 2 = –25.
Because there are ten numbers in the set, the mean of the set is –25/10 = –2.5.
The answer is –2.5.
Example Question #2973 : Sat Mathematics
If the mean of z and s is 22, and the mean of b and f is 22, what is the mean of z, s, b, and f?
22
27
17
20
22
If the average of two numbers is 22, and the average of two more numbers is 22, the average of all of them will be 22.
Example Question #21 : Data Analysis
In a set of four numbers, the second is twice the size of the first, the third is two more than three times the size of the first, and the fourth is five times the third. In terms of x, what is the mean of these four numbers?
None of the other answers
21x
x + 1.5
(21x/4) + 3
(11x/4) + 0.5
(21x/4) + 3
Begin by writing out the values of our numbers.
Number 1: x (since it is our reference point for all the other numbers)
Number 2: 2x (simple from the problem)
Number 3: 3x + 2 (two more [i.e. + 2] than three times the first [i.e. 3x])
Number 4: 5 * (Number 3) = 5 (3x + 2) = 15x + 10
Now, to find the mean, we need to add together all of these three values and divide them by four. Their sum is:
x + 2x + 3x + 2 + 15x + 10 = 21x + 12
The mean is (21x + 12)/4 = (21x/4) + (12/4) = (21x/4) + 3
Example Question #21 : Statistics
Jack traveled for 3 hours at a rate of 70 miles per hour and for 5 hours at a rate of 55 miles per hour. What was his approximate average speed for the 8-hour period, rounded to the nearest mile per hour?
61
60
59
65
70
61
You multiply the number of hours that Jack went 70 mph by 3 hours, multiply the hours he went 55 by 5 hours, and add the totals giving you a total of 485 miles. You then divide this by 8 hours, giving you 60.625, rounding to 61 mph.
Example Question #2976 : Sat Mathematics
If i = 2j = 5k, what is the average of i, j and k in terms of i?
17i/30
7i
7i/30
7i/10
17i/10
17i/30
You solve each variable in terms of i, giving you j = i/2 and k = i/5, then add both to i, giving you 17i/10 and then divide by 3 giving you 17i/30.
Example Question #22 : Data Analysis
This semester, Mary had five quizzes that were each worth 10% of her grade. She scored 89, 74, 84, 92, and 90 on those five quizzes. Mary also scored a 92 on her midterm that was worth 25% of her grade, and a 91 on her final that was also worth 25% of her class grade. What was Mary's final grade in the class?
91
87
85
93
89
89
To find her average grade for the class, we need to multiply Mary's test scores by their corresponding weights and then add them up.
The five quizzes were each worth 10%, or 0.1, of her grade, and the midterm and final were both worth 25%, or 0.25.
average = (0.1 * 89) + (0.1 * 74) + (0.1 * 84) + (0.1 * 92) + (0.1 * 90) + (0.25 * 92) + (0.25 * 91) = 88.95 = 89.
Looking at the answer choices, they are all spaced 2 percentage points apart, so clearly the closest answer choice to 88.95 is 89.
Example Question #21 : How To Find Arithmetic Mean
A function f(x) = 3x + 2 is defined for all values of x. What is the average value of the function when x can only take the values {–1, 0, 2, 5, 9}, each with equal probability?
3
6
13
11
9
11
Let's find out what values the function takes for the given x-values.
f(–1) = 3(–1) + 2 = –1
f(0) = 2, f(2) = 8, f(5) = 17, f(9) = 29
We're told that the function takes these different values with equal probability, so to find the average we need to sum up the f(x) terms and divide by the number of terms, 5.
average = (–1 + 2 + 8 + 17 + 29) / 5 = 11
Example Question #21 : Statistics
Daria plays darts often. She scores 25 points 1/5 of the time she plays. She also scores 50 points with probability 3/5, and 0 points with probability 1/5. What is the average number of points Daria scores when she plays darts?
35
30
40
25
20
35
To find the average number of points, we need to multiply the points by their corresponding weights and sum them up.
Average = 1/5 * 25 + 3/5 * 50 + 1/5 * 0 = 35.
Example Question #2981 : Sat Mathematics
Mrs. Hovsepian teaches 5 different math classes.
The first class contains 42 student. The second class has 38 students. The third class has 67 students. The fourth class has 25 students. The fifth class has 28 students.
What is the mean number of students per class?
47
43
42
38
40
40
To get the mean we must add up all of the students and divide by the number of classes. When we add them all up there are 200 total students.
Example Question #31 : Arithmetic Mean
Find the arithmetic mean of the following set of numbers:
The mean is adding all the numbers then dividing by the number of items.
In this case we have,
where
When this happens, the average is
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