SAT Math : Statistics
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Example Question #41 : How To Find Arithmetic Mean
Choose the statement(s) that holds true for the following set of data:
{50, 63, 54, 59, 67, 61, 54, 68, 58, 66}
I. The median is 60.
II. The mean is 60.
III. There is no mode.
II is only true.
I, II, and III are true.
I is only true.
I and II are true.
I and III are true.
I and II are true.
List the numbers in order to find the median: {50, 54, 54, 58, 59, 61, 63, 66, 67, 68}. The middle numbers are 59 and 61 so their average is 60 for the median of the data set making statement I true. Add the list of numbers and divide by 10 to get a mean of 60, making statement II true. There is a mode of 54 so statement III is false.
Example Question #41 : How To Find Arithmetic Mean
Jim drives for 1 hour at 33 miles per hour, 3 hours at 45 mph and travels at 60 mph for 30 minutes. What is his average speed during the trip?
To find the average speed, add up the total distance traveled
and divide by the total time (4.5 hours).
Example Question #42 : How To Find Arithmetic Mean
Susie drove 100 miles in 2 hours. She then traveled 40 miles per hour for the next hour, at which point she reached her destination. What was her average speed for the entire trip?
47 miles per hour
48 miles per hour
45 miles per hour
50 miles per hour
43 miles per hour
47 miles per hour
Distance = Rate * Time
We are solving for the rate. Susie was driving for a total of 3 hours. The distance she traveled was 100 miles in the first leg, plus 40 miles (40 miles per hour for one hour) in the second leg, or 140 miles total. Use the total distance and total time to solve for the rate.
140/3 = 46 2/3 miles per hour (roughly 47 miles per hour)
Example Question #44 : Statistics
If the average (arithmetic mean) of 
The mean will be equal to the sum of the given values, divided by the number of given values.
Use this equation to solve for 
Multiply both sides by 3.
Divide both sides by 9.
Example Question #41 : Statistics
On Monday the temperature is 58 degrees, on Tuesday it is 64 degrees, and on Wednesday it is 70 degrees. On Thursday, it is five degrees hotter than it was on Monday. Friday, Saturday, and Sunday are all the same temperature as Tuesday. What is the average temperature for the week, rounded to the nearest whole degree?
Thursday is 5 degrees hotter than Monday, so on Thursday it is:
Friday, Saturday, and Sunday are the same temperature as Tuesday, so they are all 64 degrees. Now we know all the necessary information to calculate the average.
The best answer choice is therefore 64.
Example Question #42 : Statistics
What is the arithmetic mean of all of the odd numbers between 7 and 21, inclusive?
One can simply add all the odd numbers from 7 to 21 and divide by the number of odd numbers there are. Or, moreover, one can see that 14 is halfway between 7 and 21.
Example Question #41 : How To Find Arithmetic Mean
The average age of a certain group of 20 people is 25 years old. Another group of 10 people with an average age of 40 years comes in and joins the first group. What is the average age of the new group?
35
32.5
30
25
40
30
We cannot just take the average of the ages 25 and 40, which is 32.5 years old.
Instead, we need to take a weighted average, taking into account the varying number of people in each group.
Take the average age of each group and multiply it by the number of people in that group and then take the sum. Next divide by the total number of people to get the weighted average age of the new group.
(20 * 25 + 10 * 40)/30 = 30
Example Question #41 : Statistics
In Stacey's history class, her overall class grade is the arithmetic mean of 5 exams. If her average on the first 4 tests is 85, and she scores 100 on her last exam, what will her final grade in the class be?
84
92
96
100
88
88
The arithmetic mean can be though of as (total number of points)/(total number of tests). The total number of points that Stacey earned is 
Stacey's final grade is 
Example Question #42 : Arithmetic Mean
The average of 12, 11, 10, 16, and x is 12. Solve for x.
9
13
10
12
11
11
The average is the sum of the numbers divided by the total number of terms. Therefore, 
We can multiply each side by 5 leaving us with 
We can simplify this equation to 
After subtracting 49 from both sides, we are left with 
Example Question #51 : Data Analysis
A certain group of 12 students has an average age of 17. Two new students enter the group. The average age of the group goes up to 18. What is the average age of the two new students that came in?
28
24
12
16
20
24
If 12 students have an average age of 17, we can say 
Therefore the sum of the students' ages is 12 x 17 = 204.
Two students enter the group, so the total number of students goes up to 14.
We are told that the new average age is 18.
Thus, the sum of the ages of the 14 students is 14 x 18 = 252.
The difference of the two sums gives us the sum of the ages of the two new students:
252 - 204 = 48
The average age of the two new students is then 48/2 = 24.
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