## Difference Between Mean and Median

*Mean and median** are two commonly used terms in mathematics. Mean is like an average of a given number. It sums up the numbers and divides them with the count of numbers which provides us with the mean. Median, on the other hand, returns the middle number from the whole data set, if even. It adds the two middle numbers and divides them by 2, giving us the median.*

Both are used to measure central tendency and large data sets where analysis needs to be drawn, and results are interpreted. Finally, mean, median, and mode are three measures of averages that show the dispersion of the data is from the mean or the average. These methods are used in statisticsStatisticsStatistics is the science behind identifying, collecting, organizing and summarizing, analyzing, interpreting, and finally, presenting such data, either qualitative or quantitative, which helps make better and effective decisions with relevance.read more widely, whereas the mean value of the data is the most commonly used method among the three.

### What is Mean?

Mean is a simple sum of all observations divided by the number of observations in an array. For example, if we talk about the average height or the mean height of a group of 5 people, we would calculate the mean by summing the height of 5 people divided by the number of people, i.e., 5.

#### Formula

**Mean Formula = (Sum of all the observations/number of observations)**

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Source: Mean vs Median (wallstreetmojo.com)

### What is the Median?

Median is the middle number in the data array set, which separates the higher set of the data from the lower. Therefore, the data needs to be arranged in ascending order first to calculate the median of the data. Then, when the data set has cardinality, the mean of the middle two numbers in the data set needs to be taken. However, these two methods are often used interchangeably.

#### Formula

**Median formula** = (n+1)/2

when n is an odd number

**Median = [(n/2) + {(n/2)+1}] / 2**

when n is an even number

### Mean vs Median Infographics

Let us see the top differences between mean vs. median.

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Source: Mean vs Median (wallstreetmojo.com)

### Mean vs Median Key Differences

- Mean is simple to use and can be applied to any data array set, whether even or odd. Median is slightly complex to use, and the data set needs to be arranged in the ascending or descending order first before calculation.
- The mean is generally used for normal distributionsNormal DistributionNormal Distribution is a bell-shaped frequency distribution curve which helps describe all the possible values a random variable can take within a given range with most of the distribution area is in the middle and few are in the tails, at the extremes. This distribution has two key parameters: the mean (µ) and the standard deviation (σ) which plays a key role in assets return calculation and in risk management strategy.read more, whereas the median is used for the skewed distributions data set.
- The mean is simple, but it is not robust because it can contain outliers in the distributions and sometimes does not give the user the correct results for interpretation. On the other hand, the median method is robust and is better suited for skewed distributions to derive the central tendencyCentral TendencyCentral Tendency is a statistical measure that displays the centre point of the entire Data Distribution & you can find it using 3 different measures, i.e., Mean, Median, & Mode.read more of the date set and will give the user many accurate results when compared to mean
- There is only one formula of mean – the sum of all the observations divided by the numbers of observations. At the same time, the median has two formulas. One of the odd where just the middle numbers from the dataset become the median. But when we have an even data set, the middle of the two values are picked and divided by 2, giving us the median of the even data set.

### Mean vs Median Comparative Table

Mean | Median |

The mean is computed by adding all the values in the data array, divided by the number of observations. | Median is the exact middle value of the data set. It can be computed by arranging the data set in ascending order and then finding or picking out the central value from the data set. |

It is more widely used in the industry due to easy computation of the average, and it gives us a quick number. | It is not used often in the industry, but it is more accurate than mean, just a simple sum of numbers. |

It is generally used for usually skewed data sets, i.e., normal distribution. | It is convenient to describe the dataset with a significant skewness in the data or when the data has a long tail. It is used widely where the outliers carry considerable weight in the data where the mean is not a suitable method of calculation. |

It is not a robust tool for a calculation to derive the central tendency. | It is a robust tool as it determines the weight in the data, generally high weight at the longer tails. |

It is susceptible to outliers. | It is much less affected by the outliers. |

It is simple to use. | It is complex. |

It cannot be calculated for categorical data, as it cannot sum the values. | It cannot be identified for categorized nominal data as it cannot logically order it. |

### Conclusion

Apart from the mean and median, one more method is often used to measure central tendency: the mode. A mode is a value that most frequently occurs in the data set. It has an advantage over the mean and median and can be found for numerical and categorized data sets.

Despite the existence of mode and median and their superiority of better results and analysis over the mean, the mean is still the most appropriate measure of central tendency, especially if the data set is a normal distribution and the data is usually skewed.

As a good analyst, the central tendency should be measured with all three data methods. Then, the variance in the analysis should be pondered and carefully analyzed to produce better and more accurate results in the data set.

### Recommended Articles

This has been a guide to Mean vs Median. Here we discuss the top differences between them along with infographics and a comparison table. You may also have a look at the following articles –

- Calculate Weighted Mean
- Normal Distribution Graph Excel
- Variance and Standard Deviation
- Geometric Mean vs. Arithmetic Mean

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