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How To Calculate The Mean, Median, And Mode – Formula, Solved Examples

How To Calculate The Mean, Median, And Mode

Before going to know How To Calculate The Mean, Median, And Mode, it is very important to know their meaning and concept separately. The first measure of central tendency is the mean, which is simple known as means average. Second measure is called as median, which means middle number when listed in order from least to greatest. Another and last measure of central tendency is mode which means the numbers which comes maximum time.

Actual meanings of Mean, Median, And Mode

 The mean is the average of a data set.

 The mode is the most common number in a data set.

 The median is the middle of the set of numbers.

Mean, median, and mode are three kinds of averages. In Statistics there are many averages but the most important are Mean, median, and mode. In this article of www.recruitmentinboxx.com, individuals can easily understand measure of central tendency, Formula along with solved examples. Without Mean, Median, And Mode calculation methods, it will be impossible to understand and calculate much of the data we use in daily life.

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How To Calculate The Mean, Median, And Mode


If you want to talk about statistical averages then it is commonly known as the mean that considered as the average of a data set. To know How To Calculate The Mean have a look: You need to add all of your numbers together. Subsequently, divide the sum by however the numbers you added. The result is your mean or average score.

For example, let’s say you have four test scores: 15, 18, 22, and 20. To find the average, you would first add all four scores together, after that you need to divide the sum by four. Mean of 15, 18, 22, and 20 is 18.75. Written out, it looks something like this:

(15 + 18 + 22 + 20) / 4 = 75 / 4 = 18.75 (The average would be 19)

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As we have discussed above that the median is the middle value in a data set. If you want to calculate median then you are advised to place all of your numbers in increasing order (छोटे से बड़ा). Candidates who are going to calculate median firstly they must check the series of numbers such as even or odd. If you have an odd number of integers, then find the middle number on your list.

For example, you have this series 3, 9, 15, 17, 44, then according to this series, the middle or median number is 15:

If you have an even number of data points, calculating the median requires another step or two. First, find the two middle integers in your list. Add them together, and then divide by two. The result is the median number.

For example, you have this series: 3, 6, 8, 12, 17, 44, According to this example, the two middle numbers are 8 and 12. Now you need to written out, the calculation would look like this:

(8 + 12) / 2 = 20 / 2 = 10, in this instance, the median is 10.

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Unlike the median and mean, the mode is about the frequency of occurrence. There can be more than one mode or no mode at all; it all depends on the data set itself. For example, let’s say you have the following list of numbers:

3, 3, 8, 9, 15, 15, 15, 17, 17, 27, 40, 44, 44

As per above given series, the mode is 15 because it is the integer that appears most often. However, if there were one fewer 15 in your list, then you would have four modes: 3, 15, 17, and 44.

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Formulas of Mean, Median, And Mode

The Mean

Formula of Mean is: x¯¯¯=∑xN


  • ∑ represents the summation
  • X represents scores
  • N represents number of scores.

The Median

If the total number of numbers (n) is an odd number, then the formula is given below:

For Odd Numbers series: Median= (n+1n)thterm

If the total number of the numbers (n) is an even number, then the formula is given below:

For Even Numbers series: Median= (n2)thterm+(n2+1)thterm2

The Mode

The mode is the most frequently occurring score or value.

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Mean, Median, And Mode Solved Examples

Question: Find the mean, median, mode, and range for the following list of values: 13, 18, 13, 14, 13, 16, 14, 21, 13


Given sequence: 13, 18, 13, 14, 13, 16, 14, 21, 13


The mean is the usual average, so:


Note that, the mean isn’t a value from the original list. This is a common result. You should not assume that your mean will be one of your original numbers.


The median is the middle value, so to rewrite the list in order:

13, 13, 13, 13, 14, 14, 16, 18, 21

There are nine numbers in the list, so the middle one will be


= 5th number, So the median is 14.


The mode is the number that is repeated more often than any other, so 13 is the mode.


The largest value in the list is 21, and the smallest is 13, so the range is 21 – 13 = 8.

  • Mean: 15
  • Median: 14
  • Mode: 13
  • Range: 8

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