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What is the Mode and How Do I Find It?

In these set of lessons, we're learning about the measures of central tendency. We'll learn about mode, median, mean, range, standard deviation (both the overall concept and the method of calculation), and statistical significance.

The mode is the most common value in a data set. In other words, the mode is the value that shows up the most in a set of numbers or variables. Mode is the number you find at the highest frequency in a number of data points.

Just like when you're trying to find the median, the first thing you need to do is put the values in your data set in order.

You can certainly try to find the mode without putting the values in order. This might not be so bad if the data set is small. But good luck with that approach if you've got a big data set...

Save yourself the headache. Put the values in order.

$35$ shows up three times, which is more times than any other value! So, $35$ is the mode!

$14$ shows up four times, which is more times than any other value! So, $14$ is the mode!

What is there is No Mode?

Consider the dataset $\{1,2,3,4\}$. What is the mode?

There is no "most common number", so we say that this data has no mode.

Now, consider $\{1,1,2,3,4,4\}$. We notice that the most commonly occurring numbers are $1$ and $4$, which both occur twice. So, we say that the dataset has two modes, which are $1$ and $4$.

Graphically, you will easily be able to determine the mode in a histogram showing frequency. A frequency table and frequency distribution will also show you the mode.

(Video) Find the Mode of a Set of Data

by MySecretMathTutor

This video by MySecretMathTutor defines the mode of a data set.

$\large{\text{Summary}}$

The Mode of a distribution is the value shared by the largest group of data points which share a single value. Data sets may have many modes, or they may have no modes. For now, we will consider the Unimodal distributions, which have only one mode.

Put more simply, the Mode is the most common number in a data set.

Knowing the mode is useful because it tells you where most of the data is. In some Unimodal data sets, the mode is also very close to the mean and the median. The mode pulls these measures towards itself by the weight of its numbers.

Mode

The mode of a data set is the value with the highest frequency. In other words, it's the value that appears the most times!

Note: There can be more than one mode if multiple data points have the same highest frequency.

Click here for more information on when to use the mode!

To find the mode of the data set $8, 8, 8, 6, 2, 5, 5, 0, 5, 2, 5$ we can first sort the data. $$0, 2, 2, 5, 5, 5, 5, 6, 8, 8, 8$$

Next, find the value with the highest frequency. $5$ occurs four times...the most number of times out of all the data points. So, $\boxed{5}$ is the mode.

To do practice with word problems, check out this lesson. Another measure of central tendency is standard deviation, which we'll learn about later.