Basic Arithmetic : Mode

Study concepts, example questions & explanations for Basic Arithmetic

varsity tutors app store varsity tutors android store

Example Questions

Example Question #425 : Statistics And Probability

Find the mode of the following set of numbers: \(\displaystyle 34, 65, 2, 8, 46, 89, 23, 67, 23, 45, 12, 56, 12, 5\).

Possible Answers:

\(\displaystyle 34\)

\(\displaystyle 23\)

\(\displaystyle 12\) and \(\displaystyle 23\)

\(\displaystyle 12\)

\(\displaystyle 23\) and \(\displaystyle 34\)

Correct answer:

\(\displaystyle 12\) and \(\displaystyle 23\)

Explanation:

The mode of any set of numbers is the number that occurs the most often in set. In order to find the mode, it's easiest to start by arranging the numbers in the set from least to greatest. The set of numbers we were given is

\(\displaystyle 34, 65, 2, 8, 46, 89, 23, 67, 23, 45, 12, 56, 12, 5\)

In order from least to greatest, this set looks like:

\(\displaystyle 2, 5, 8, 12, 12, 23, 23, 34, 45, 46, 56, 65, 67, 89\)

Now that our numbers are in order, it's easier for us to see if there are any numbers that show up more than once. In this case, both \(\displaystyle 23\) and \(\displaystyle 12\) appear in the set two times, and every other number in the set appears only one time. Since \(\displaystyle 12\) and \(\displaystyle 23\) appear an equal number of times in the set as the other does, they are both considered to be modes of the set. 

So, there are two modes for our set: \(\displaystyle 12\), and \(\displaystyle 23\).

Example Question #446 : Statistics And Probability

What is the mode of this class's state exam results if the scores are the following?

\(\displaystyle 87,86,42,91,93,87,87,94,62,91,92,31,87,87\)

Possible Answers:

\(\displaystyle 87\)

\(\displaystyle 94\)

\(\displaystyle 86\)

\(\displaystyle 84\)

\(\displaystyle 31\)

Correct answer:

\(\displaystyle 87\)

Explanation:

The mode is the number that appears most often in your set. In this case we will be looking at which score appears most often. 

Mode exam

This is one simple way of organizing data to indicate the mode. Each number that appeared in the data set was written down. Each "X" written above each number indicates each time it was present in the set. We see that 87 appeared most often. Therefore, 87 is the mode of the data set. 

Example Question #21 : Mode

You take a quiz in class and are shown the results of 10 students. There were 8 questions and the score is given as 1-8. Find the mode of the following results:

\(\displaystyle (4,2,7,6,8,5,4,7,8,7)\)

Possible Answers:

\(\displaystyle 6\)

\(\displaystyle 7\)

\(\displaystyle 5.8\)

\(\displaystyle 4\)

Correct answer:

\(\displaystyle 7\)

Explanation:

To find the mode, you can make a number line and place an "x" for every occurance of a score or number. 

Mode

The mode of a data set is the value which appears most often. In this case the mode is 7 since it occurred 3 times.

Learning Tools by Varsity Tutors