SAT Math : Statistics
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Example Questions
Example Question #71 : Arithmetic Mean
If 
First Step is to write each mean equation out.
Example Question #72 : Arithmetic Mean
Based on the table, what is the the mean shoe size among the children?
To calculate the mean shoe size, first sum up all the shoe sizes and then divide by the number of children.
Looking at the table, there are five children.
Therefore the formula to calculate the mean becomes,
Example Question #73 : Arithmetic Mean
If Billy has an average of 
In order to solve this lets write two general equations that we will solve.
From the first equation, we get.
Substitute tis into the next equation,
Solve for 
Example Question #74 : Arithmetic Mean
The mean of a group of five numbers is 10. The numbers in the group are 7, 11, 23, 4, and x. What is x?
We know that the mean of the five numbers is ten. Therefore the sum of the five numbers, divided by 5, equals ten.
So,
After solving for x we learn that x equals 5.
The algebraic steps are as follows:
Example Question #1 : Median
The chart above shows the scores on two tests for five students in a science class. If John's score was equal to the mode for Test I and equal to the median for Test II, then which of the five students represents John's scores?
A
C
B
D
E
B
The mode of a set of numbers is the number that appears most frequently in that set. The median of a set of numbers is the number that appears in the middle when they are arranged in numerical order. For Test I, the mode is 85. When arranged in numerical order, the scores for Test II are:
70, 70, 80, 85, 90.
That makes the median for Test II 80. The only student in the chart with an 85 on Test I and an 80 on Test II is student B.
Example Question #1 : How To Find Median
The average (arithmetic mean) of 1, 7, 9, and n is –1. What is the median of this set?
7
4
–2
1
–4
4
If the mean is –1, then 1 + 7 + 9 + n = –4. Solving for n gives us n = –21. In numeric order, we now have –21, 1, 7, 9. As there is an even number of numbers, we average the middle two. (1 + 7) / 2 = 4.
Example Question #1 : Median
The average of 5, 10, 12, 15, and x is 11. What is the median?
13
12
11
15
12
You must first find what x is in order to find the median.
To find x, set up the following equation:
To solve the equation, first multiply both sides by 5:
5 + 10 + 12 + 15 + x = 55
Then, add up 5 + 10 + 12 + 15 to get 42:
42 + x = 55
x = 13
Now that you know what x is, you are ready to find the median. To find the median, order the numbers from lowest to highest. The median is the number in the middle.
5, 10, 12, 13, 15
Example Question #1 : How To Find Median
The monthly averaged high-and low-temperatures in Michigan are shown in the given table. What are the median monthly averaged high- and low-temperatures respectively in Michigan?
high: 58F, low: 37F
high: 60F, low: 39F
high: 56F, low: 35F
high: 46F, low: 35F
high: 56F, low: 30F
high: 58F, low: 37F
Median is the middle number when the data are ordered from least to greatest. In this case, there are 12 numbers, so, the median is the average of the middle two numbers, which are the 6th and 7th numbers in an ascending order. For the averaged high-temperature, the median is (56+60)/2=58, and for the averaged low-temperature, the median is (35+39)/2=37
Example Question #1 : How To Find Median
Find the median of the following sequence:
3, 4, 5, 6, 7, 7, 10
5
6
7
10
6
The median is the middle number in a sequence when the numbers are put in order. Since this sequence is already in order from least to greatest, we just need to find the middle number. There are 7 terms so the middle term is (7+1)/2 or the 4th term. This is 6.
Example Question #1 : How To Find Median
Find the median of the data set:
25, 37, 13, 58, 52, 83, 21, 51
13
44
70
42.5
83
44
42.5 is the mean of the data. 13 is the minimum. 83 is the maximum. 70 is the range.
To find the median, list all numbers in order:
13, 21, 25, 37, 51, 52, 58, 83
and find the middle value. In cases like this where there are two middle numbers (37 and 51), find the mean of these two numbers.
(37+51)/2 = 88/2 = 44
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