How to Find the Mode?

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Whenever one hears the term, “Measures of Central Tendency,” all that strikes is to find the mean, median, and mode. Mean, median, and mode are basically three kinds of averages.

A lot of averages are used in statistics, but these three are most commonly used. Let’s discuss what is mode and how to find the mode?

The “mode” is the value that occurs very frequently. In case no numbers are repeated, then there is no mode for the list. In short, in a series of numbers, the mode is the number that appears the most. Example: in {6, 3, 9, 6, 6, 5, 9, 5} the Mode is 6, as it occurs most often.

For a general overview, it was Karl Pearson, who invented what is the mode in math. He was one of the most influential, famous and great statisticians that existed. He also founded the world’s first Statistical University department in London.

Let’s throw some light on how do you find the mode:

Put the Numbers in Order

In order to find mode, the first and foremost step is to put the numbers in order. Just write these numbers in sequence. In case you are using a laptop or computer, use a spreadsheet program to initiate the process. It is preferable to arrange the scores from least to greatest.

Example – 7, 13, 18, 24, 9, 3, 18, 24

Solution – Now, arranging the scores from least to greatest:

3, 7, 9, 13, 18, 18, 24

Answer: The number which occurs most often is 18. Thus, the mode is 18.

how-to-find-the-mode

There is no hard and fast rule to arrange the data in order, but when large data sets are involved, arranging becomes a necessity. It eases the process and omits the frequency of making errors while calculating.

Arranging the Numbers in Excel

Working the same on the computer simplifies the process to a large extent due to the availability of extensive options. In case there are a large number of items in the data set, Excel comes with a “sort” button on the toolbar that will sort numbers from smallest to largest or largest to smallest.

  1. Type your numbers into a single column in Excel.
  2. Click “Home,” then click “Sort and Filter.”
  3. Click “A to Z” to sort from smallest to largest or “Z to A” to sort from largest to smallest.
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How to Find the Mode by Cross Method

In order to avoid ambiguous dealing and incorrect answers, organizing the data becomes a quintessential part. You can organize the data by this method too:

  1. Random look- Just have a general look at the group of numbers and cross out those that aren’t a possibility.
  2. Cross- Simply cross out the numbers that appear only once.
  3. Go again- Now, search for the numbers that appear twice and strike them off.
  4. The last step- Automatically, you will be left with the numbers that occur most often. Thus, it becomes easier for you to identify the mode.

Undoubtedly, it is a lengthy method but helps to avoid mistakes to a large extent.

Bimodal Mode

A group of numbers can have more than one mode. When a solution has two different modes, it becomes bimodal, i.e. there are two data values that tie for having the highest frequency.

Example 1 –  24,  15,  18,  20,  18,  22,  24,  26,  18,  26,  24

Solution – Arrange the data from smallest to greatest:

You will, get- 15, 18, 18, 20, 22, 24, 24, 24, 26, 26

Since both 18 and 24 occur three times, the modes are 18 and 24. This data set is bimodal.

Let’s have one more example to understand the same:

Example 2:    5, 6, 2, 5, 8, 7, 4, 9, 1, 4

Solution – Arrange the data from smallest to greatest

1, 2, 4, 4, 5, 5, 6, 7, 8, 9

Now, this set of numbers has 2 modes, 4 and 5; these numbers both occur twice, while all the other numbers occur only once.

No Mode

Sometimes, all the values in a set of data occur only once. It creates a situation of no mode.

Example – 7, 3, 8, 11, 5, 19, 4, 10

  • This group does not have a mode because all the numbers occur only once.

However, do not confuse a mode of 0 with no mode.

Example – 12, 4, 5, 0, -8, 1, 0, -3

Solution – Arrange the numbers from least to greatest:

-8, -3, 0, 0, 1, 4, 5, 12

Answer: Thus, mode of this set is 0.
In case there are more than two modes, it is a situation of “multimodal”.

Grouped Data

When the frequency of values or categories is grouped, then a different formula is applied for calculating Mode. Let’s understand first that what the modal range is:

Modal Range

The Modal Range is, basically the one that includes the Mode. Therefore, the modal range is the one that has the highest Simple Frequency.

Thus, whenever the frequency of values is grouped, then the following formula is applied for calculating mode:

Estimated Mode (M) = L + fm − fm-1                         * W
                                                    (fm − fm-1) + (fm − fm+1)
Formula’s Symbols Explanation
M= (Estimated) Mode / Modal value
F =Frequency
L=the Lowest value of the Modal Range
fm =Frequency of the Modal Range:
fm-1 =the frequency of the Range that is exactly before the Modal Range
fm+1= the frequency of the Range that is exactly next to the Modal Range
W= the size of the Modal Range

Let us take an Example-

L = 60.5

fm-1 = 7

fm = 8

fm+1 = 4

w = 5

M= 60.5 +          8-7                               * 5

(8-7) + (8-4)

= 60.5+ (1/5) x 5

= 61.5

Don’t Confuse Mode with Mean and Median

Mean, median and mode are the three main methods of calculating averages. People tend to confuse the three, very often. However, these three concepts are entirely independent of each other.

So, just go through the implications of each one, once and avoid the confusion between the three of them.

The median is the middle number of a set of data, and the mean is calculated by adding up all the numbers in a data set and then dividing that sum by the total of numbers that are being added.

Conclusion

Out of all the averages, how to find the mode is the simplest, and it is easy to understand. It is useful for qualitative data and can be located graphically.

However, one of the main issues with the mode is that it is stable for large values only and is not capable of further mathematical treatment. Reliability is also a problem as sometimes, the data has one or more than one mode and sometimes the data have no mode at all.

It will completely suffice to say that “Practice makes a man perfect.” So just choose the average based on the data you are studying and practice the calculations, and in a nick of time, you will be the master of calculating the mode.

rishika

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