Difference Between Mean and Median (With Table)

Mean and Median are two terms that are used in mathematics. Mean and median is part of statistics that are used in many industries to analyze, interpret and present empirical data. The mean is the average of the given values while when we find the Median we get the center of the set of data.

Mean vs Median

The main difference between mean and median is that both have different formulas and are different methods to find out the center of a given data set. Both mean and median are measures that are used to find the central tendency of a data set along with one more term which is called mode. In a dataset, the mode is the value that appears the most.

Mean is the value that occurs when we sum up all of the values and divide that sum by the number of values in a dataset. It is the average of the values given in a dataset. It is mostly used in sports, research activities, and to calculate the overall performances of a student or an employee, etc.

The Median is the center of a group of data. It is used to find accurate results. Median is used in daily life problems like grouping data, buying a property, balance the home budget, explicating the poverty line, etc.

Comparison Table Between Mean and Median

Parameters of ComparisonMeanMedian
DefinitionMean is the average of a given set of data.The median is the middle or center of the data.
Formulam = sum of terms/number of termsM = (n+1)/2, term for an odd data set.   M = [n/2 term + (n/2 +1) term ] / 2 , for even data set.
UsesIn sports, to calculate overall performances of a student or an employee, etc.In daily life problems like grouping data, buying a property, etc.
SkewnessThe mean is susceptible to skewed data.The median is not much affected by Skewed Data.
Central TendencyMean is a well-known measure for a central tendency.Mean is affected by outliers due to which median is used and is a much better option for a central tendency.

What is Mean?

Mean is the value that we get when we calculate the average of the data set. It is a measure we use to find the central tendency of the data set. It is used in many statistical calculations. It is the basis of statistics. Mean is used to find values in R charts, X Bar charts, etc.

The mean of a set of data is found by adding all the values and then dividing them by the number of values there are. The formula for mean is :

Mean, m = sum of terms/number of terms

For example: Here is a set of data 10, 20, 40, 50, 70, 90.

So the mean for the above data will be, m= 10 + 20 + 40 + 50 + 70 + 90 / 6 = 280 / 6 = 46.66. We added all the terms and then divided the total with 6 as the values were six in number.

That means, basically the mean is the average of the data given. There are different types of mean, however, there are only two main types: Arithmetic mean and geometric mean. The formula we looked at above is the main basic formula of mean which is usually used. And is called the arithmetic mean.

What is Median?

The median is the middle of the data set i.e. the same amount of values above and below. The data set is first set in ascending order. The terms have to be set from the lowest to the highest values, then the middle is found out by the below formula which will be our median:

Median = (n+1)/2, term for an odd number of terms in a data set. That means that for an odd data set the middle term will be the median.

Median = [n/2 term + (n/2 +1) term ] / 2 , for even number of terms in a data set. That implies that the average of the middle two terms will be the median for an even data set.

For example, (i) Odd data set = 2, 5, 6, 7,6, 5, 3

Lowest to highest : 2,3,5,5,6,6,7 ; the median will be (n+1)/2 = 7+1/2 = 4th term. The 4th term is 5, so it is the median.

(ii) Even data set = 2,5,6,7,9,8,6,3

Lowest to highest : 2,3,5,6,6,7,8,9

Median = [(8/2) + (8/2 +1) ] /2 = [4th term + 5th term] / 2 = 6+6 /2 = 6. 6 is the median for this data set.

Indeed, The Median divides the dataset equally. It separates the data set which give us the same number of terms above and below the median.

Main Difference’s Between Mean and Median

  1. Mean is the average of a data set while the median is the middle of the data set.
  2. The formula for mean is, m = sum of terms/number of terms. The formula for the median is (n+1)/2, term for an odd data set and [n/2 term + (n/2 +1) term ] / 2 , for even data set.
  3. By the mean formula, we directly found the value which will be our answer, while in the median formula we found which term will be our median. That value of that particular number of a term will be the median.
  4. Mean is affected by skewed data while Median doesn’t get affected much and therefore median provides a typical representative value and is more preferred.
  5. Mean and median are both measures to find the central tendency however median is preferred more than the mean to find accurate data.

Conclusion

Mean and median are mathematical terms used in statistics to measure central tendency in a data set. Mean is the average of a dataset while on the other hand median is the middle of the data set. The median is the term that is the exact center of the data, which separates the higher half from the lower half of a dataset.

They are mostly used by insurance analysts in the healthcare industry. Mean and median both are important terms in statistics however median is said to give a more typical value. Median is more eccentric to find the center of a group of data as it describes the data.

References

  1. https://link.springer.com/article/10.1186/1471-2288-5-13
  2. https://link.springer.com/article/10.1007/s10649-006-7099-8
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