How to Find the Mode of a Set of Numbers

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In statistics, the mode of a set of numbers is the number that occurs most often in that set . A dataset does not necessarily have only one mode – if two or more values are thought to be the most common, then the data set can be called bimodal or multimodal – in other words , all the most common values are the mode of the set. To learn more about the process of determining the mode of a data set, see Step 1 below to get started.

Table of Contents

Find the Mode of a Dataset

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List the numbers in your data set. Modes are usually derived from sets of statistical data points or lists of numerical values. So to find the mode, you need to have a set of data to look for. It’s hard to calculate the mode value just by visualizing it except for very small data sets, so in most cases the wisest way is to write (or type) your data set out. . If you work with paper and pencil, simply write down the values in the data set in order, whereas if using a calculator you may have to resort to the Excel program.

The process of finding the mode of a data set is easier to understand when illustrated with an example. In this section, let’s use the following set of values as an example: {18, 21, 11, 21, 15, 19, 17, 21, 17} . In the next steps, we will find the mode of this set.

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Arrange the numbers in order from smallest to largest. The wise way is to sort the values of the data set in ascending order. Although this is not required, it makes the process of finding the mode easier because it groups similar values together. For large data sets, this is really necessary, because sorting through long lists and remembering how many times each number appears in the list is very difficult and can lead to errors.

If you work with paper and pencil, taking notes can save time in the long run. Go through the set of numbers to see which is the smallest, and once you’ve found it, start the new dataset with that smallest number, followed by the second smallest, third, etc. Make sure you write each number equal to the number of times it occurs in the original data set.
With a calculator, you can sort lists of values in order from smallest to largest with just a few clicks
In the above example, after sorting, our new list will be : {11, 15, 17, 17, 18, 19, 21, 21, 21} .

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Count the number of times each number is repeated. The next step is to count the number of times that each number appears in the set. Find the value that occurs most often in the data set. For relatively small data sets with points sorted in ascending order, it is relatively simple to find “clusters” of similar values and count their occurrences.

If you work with paper and pencil, keep your count in mind, writing down how many times each value appears on each cluster of numbers. If you use the excel program on your computer, you can do the same by writing them in the cell next to them, or use one of the program’s functions to count the data points.
In our example, ({11, 15, 17, 17, 18, 19, 21, 21, 21}), 11 occurs once, 15 occurs once, 17 occurs twice, 18 occurs once, 19 appears once, and 21 appears three times . 21 is the most frequent value in this data set.

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Determines the value that occurs most often. Once you know how many times each value appears, find the value with the most occurrences. This is the mode of your dataset . Note that there can be more than one mode in a data set . If two values have the same maximum number of occurrences in the set then the set is bimodal (two modes), if there are three such values then the set is trimodal (three modes), and so on.

In the above example, ({11, 15, 17, 17, 18, 19, 21, 21, 21}), since 21 occurs most often, 21 is mode .
If another value other than 21 also occurs three times, (such as an extra 17 in the set), then 21 and this number will both be modes.

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Don’t confuse mode with mean or median. The three statistical concepts that are often mentioned together are mean, median, and mode. Because these concepts have similar-sounding names, and because in a data set a value can sometimes play more than one role in these numbers, it’s easy to confuse them. However, regardless of whether your data set has a mode or not, it always has a median or mean. It is important to understand that these three concepts are completely independent of each other. See below:

Mean of a data set is the mean value of that set. To find the mean, add all the values in the set together, then divide the sum by the number of terms in the set. For example the initial set of numbers ({11, 15, 17, 17, 18, 19, 21, 21, 21}), the mean will be 11 + 15 + 17 + 17 + 18 + 19 + 21 + 21 + 21 = 160/9 = 17.78 . 9 means there are 9 digits in the set.

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The median of a data set is the “middle number” that divides the small and large values of that set into two equal halves. Using the above example, ({11, 15, 17, 17, 18, 19, 21, 21, 21}) 18 is the median since it’s the middle number – there are exactly four larger numbers and four smaller numbers. It. Note that if the number of values in the set is even, the median is the average of the two middle numbers.

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Find Mode in special cases

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In data sets where each value has the same number of occurrences, there is no mode. If the values in a given set all appear the same number of times, this data set has no mode because no number occurs more than the other. For example, data sets in which each value occurs only once do not have a mode. The same is true for data sets with values that appear twice, thrice, and so on

If we change the example dataset to {11, 15, 17, 18, 19, 21} so that each value appears only once, this dataset now has no mode . This is similar if we change the data set so that each value appears twice: {11, 11, 15, 15, 17, 17, 18, 18, 19, 19, 21, 21}.

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The mode of a non-numeric data set can be found in the same way as a numeric data set. In general, most data sets are quantitative – they contain data in numerical form. However, some data sets contain information that is not represented as numbers. In these cases, “mode” is still the value that occurs most often in that data set as it is in the numeric data set. ^{[1] X Research Source} In these cases, finding the mode is possible while finding the median or mean is not.

Take an example in the biological census to determine the tree species of the area. The data set for trees in the area is {Bang, Phuong, Bang, Thong, Bang, Bang, Phuong, Phuong, Thong, Bang}. This type of data set is called a named dataset because data points are distinguished based solely on their names. The mode of the dataset is Bang because it occurs the most (five times while Phuong appears three times and Thong twice).
In the above example, you cannot calculate the mean or median because the data points are not numeric.

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For single-mode symmetric distributions, the mode, mean, and median coincide. As noted above, mode, median, and/or mean can overlap under certain circumstances. In those cases if the density function of the data set forms a perfectly symmetric curve with one mode (such as a Gauss Curve or a “Bell” curve), then both the mode, mean, and median will be same value. Because the distribution function will graph the relative occurrences of the data points, the natural mode will be in the middle of the symmetric distribution curve, since this is the highest point of the graph and corresponds to the value most popular. Because the data set is symmetric, this point on the graph will correspond to the median (the middle value of the data set) and the mean (the mean of the data set).

Consider the following example {1, 2, 2, 3, 3, 3, 4, 4, 5}. If we graph the distribution of this data set, we get a symmetric curve that has a height of 3 at x = 3 and decreases to 1 at x = 1 and x = 5. Since 3 is the value The most frequent value, it is mode . Since the value between 3 of the set has 4 values on either side, 3 is also the median . Finally, the mean of the set is 1 + 2 + 2 + 3 + 3 + 3 + 4 + 4 + 5 = 27/9 = 3, which means that 3 is still the mean .
The exception to this rule is symmetric data sets with more than one mode – in this case, since there is only one median and mean for that data set, neither of the modes will coincide with the other points. .

Advice

You can have more than one mode.
If all numbers appear only once, there is no mode.

Things you need

Paper, pencil, and eraser

Steps

Find the Mode of a Dataset

Find Mode in special cases

Advice

Things you need

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