SAT Math: Statistics and Frequency Tables

Today, we’re going to look at data that is presented in a frequency table. Before we do that,  however, let’s review the different descriptive statistics that you might see on the SAT Math test.

Mean – When people say they are finding the average, what they are usually finding is the mean, which is also called the arithmetic mean. To find the mean, you add up all of the data points and divide by the number of numbers.
Median – The median is the middle number when the numbers are ordered from least to greatest. If you have an even number of numbers, there is no “middle” number. In this case, the median is the mean of the two middle numbers.
Mode – The mode is the number that occurs the most frequently. It is possible to have more than one mode if there is a tie for what occurs most frequently. If each of the numbers appears only once, then we say there is no mode.
Range – The range is the difference between the largest number and the smallest number.

Now, let’s look a few problems that involve data that is presented to you in a frequency table.

The next three questions refer to the data presented in the table below. 

A survey of 15 elementary students asked them how many pets they have. Their responses are summarized in the table below.

1.  What is the mean number of pets that the students have?

(A)  1.4
(B)  1.6

(C)  1.8
(D)  2.0
(E)  2.5

2.  What is the median number of pets that the students have?

(A)  1
(B)  1.5
(C)  2
(D)  2.5
(E)  3

3.  What is the mode of the data presented in the table?

(A)  1
(B)  2
(C)  2.5
(D)  3
(E)  There is no mode for the data in the table.

To find the mean, we need to know how many total pets the students had. We can find that by multiplying the number of students by the number of pets for each row of the table. For instance, there were 2 students who had 3 pets, so that’s a total of 2(3) = 6 pets for that row. The calculation would look like this:

0(2) + 1(7) + 2(3) + 3(1) + 4(2)
= 0 + 7 + 6 + 3 + 8
= 24 total pets

Now divide the number of pets by the number of students: 24/15 = 1.6. The mean number of pets is 1.6 and the correct answer to the first question is Choice B.

To find the median, you need to list all of the numbers in order and find the middle number. Make sure you take into consideration that many of the numbers occur more than once. The median is not simply 2 because that number is in the middle of the table. Here are all the students’ answers listed in order:

0  0  1  1  1  1  1  1  1 2  2  2  3  4  4

Counting in from each side, you will see that the middle number (the 8th term in the list) is 1, so the correct answer to the second question is Choice A.

The mode is the number that appears most frequently. What answer did the students give more than any other? From the table we can see that more students had one pet than any other number of pets. The mode is 1 and the correct answer to the third question is Choice A.

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