Difference between Median and Average

Average and median are two basic terms that are used in statistics very often. Median is the middle value in a set, whereas average is an arithmetic mean of set of numbers.

Median and Average are two essential terms that are used in statistics, and they are used very often. In this article, we will discuss Median vs. Average. The fundamental difference between Median and Average is that the Median is the middle value, whereas the Average is the arithmetic mean of values.

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Table of Content

• Median vs. Average
• What is the Median?
• What is an Average?
• Key difference between Median and Average

Median vs. Average

Parameter	Median	Average
Definition	Median is the middle value in the number set.	It is an arithmetic mean of set of a number.
Uses	Find the central tendency of a skewed distribution.	Find the central tendency of a normal distribution.
Extreme Values	Preferred	Not Preferred
Formula	n is oddMedian = ((n + 1)/2) th termn is even Median =( (n/2) th term + (n/2 + 1)th term) / 2 where, n is number of element in set	sum of data values / number of data values
Example	1, 2, 3, 4, 5, 6, 7, 8, 9Median = 5	1, 2, 3, 4, 5, 6, 7, 8, 9 Mean = (1 + 2 + 3 +  4 + 5 + 6 + 7 +  8 + 9) / 9 = 5

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What is the Median?

Definition

In any given set, median is the middle value of that dataset when they are sorted (either ascending or descending).

• It separates the set in two equal halves.
• Median is not much sensitive to the outliers.

Formula

Let there are n elements in any set, then

• When n is odd:

Median = ((n + 1)/2) th term

• When n is even:

Median = ( (n/2) th term + (n/2 + 1) th term) / 2

Now, let’s take some example to know how these formula can be used:

Example

1. Find the median of {3, 6, 5, 11, 8, 5, 7, 3, 9}

The given set has 9 elements, and the elements are not sorted, so let’s arrange them in ascending order.

{3, 3, 5, 5, 6, 7, 8, 9, 11}

Since, number of element is 9

Hence, Median = ((9 + 1)/2)th element = 5th element = 6

therefore, Median value of the given set is 6.

2. Find the median of {2, 2, 5, 8, 11, 150}

Elements of the given set are already sorted, and the number of element = 6

Hence, Median =( (6/2)th term + ((6/2) + 1)th term )/2 = (3rd term + 4th term)/2 = (5 + 8)/2 = 6.5

therefore, Median value of the given set is 6.5.

Read Also: Skewness in Statistics

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What is an Average?

Definition

Average is defined as the mean value, equals to 

sum of all observation / number of observation

• Average is also known as Arithmetic Mean
• It is highly sensitive to the outliers
• Mainly, used to find the central tendency of a normal distribution
  • For a Normal Distribution
    • Mean = Median = Mode

Formula

Let there are n elements in any set, then:

Average =sum of data values / number of data values =  (x₁ + x₂ + x₃ + x₄ + ……. + x_n) / n

Example

3. Find the average of {3, 6, 5, 11, 8, 5, 7, 3, 9}.

Average = (3 + 6 +  5 + 11 + 8 + 5 + 7 + 3 + 9) / 9 = 57 / 9 = 6.34

Therefore, Average = 6.34

4. Find the median of {2, 2, 5, 8, 11, 150}.

Average = (2 + 2 + 5 + 8 + 11 + 150) / 6 = 178 /6 = 29.67

Therefore, Average = 29.67

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Key differences and similarities between Median and Average

• Average and Median both are “Measures of Central Tendency”.
• Average is calculated by adding up all the individuals and dividing by total number of observations, whereas median is calculated by choosing the “middle value” after arranging all the numbers either in ascending or descending order.
• Median finds the central tendency of skewed data, whereas Average is used to find the central tendency of normal distribution.
• Median is no much sensitive to the outlier, whereas Average is highly sensitive to the outliers.

Read Also: Conditional Probability

Read Also: Central Limit Theorem

Conclusion

In this article, we have briefly discussed median vs average with examples.

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