Difference Between Mean Median And Mode
Difference between mean median and mode can be understood from the different ways of calculations of the data. Only the mean involves mathematical calculation, and the median, the mode is obtained by simple observation of the data values. All the three measures of mean median and mode are useful based on the situation and also based on the given data. Difference between mean median and mode is useful for calculations and for right usage of mean median and mode based on the situation.
Let us know more about the individual difference between a set of these central tendencies to more clearly understand the difference between mean median and mode.
What Is The Difference Between Mean Median and Mode?
The difference between mean median and mode would help us understand the ways to summarize the given data. Mean, median, and mode are the three parameters that summarize the given data, and helps in the right representation of data with a single numeric value. Mean is the average of the data and it takes into account all the data points. Median is the data point that is falling in the mid of the given data, with an assumption that the data has been arranged in a sequence. And mode is the most frequently occurring data point.
Among the mean, median, and mode, only the mean includes an arithmetic operation of addition and division, but median and mode do not include any arithmetic operation. Median and mode are found based on the arrangement of the data, and the observation of the data. Mean is the average of the given data, where all the given numbers are added, and then divided with the count of the numbers. For calculation of median, the data is first arranged in ascending or descending order, and then the middlemost value is picked as the median of the given data. The mode is the data point that is occurring most frequently or the maximum number of times.
Let us look at a few examples to help us more clearly understand the difference between mean median and mode. The mean of the numbers 4, 5, 7, 11 is mean = (4 + 5 + 8 + 11)/4 = 28/4 = 7. Median of the data 11, 7, 3, 5, 12, 9, 22, 44, 36, 25, 31 is obtained by arranging this data in ascending order such as 3, 5, 7, 9, 11, 12, 22, 25, 31, 36, 44, and then pick the middlemost value, the value of median is equal to 12. And for the data 13, 17, 22, 37, 56, 17, 29, 34, 13, 17, the value of 17 has the highest frequency as it occurs 3 times in the data, and the mode of this data is 17.
Here we aim at first understanding the difference between two parameters at a time such as the difference between mean and median, the difference between mean and mode, the difference between median and mode, which would help us to clearly analyze and understand the difference between mean median and mode. Let us now look at the difference between two parameters at a time, in the below paragraphs.
Difference Between Mean and Median
Mean is obtained by adding all the values and then dividing it with the number of values. The median is obtained by arranging all the values in either in ascending or descending order and then taking the middle most value. The following points help in clearly understanding the difference between mean and median.
 Mean is the mathematical average and median is the positional average.
 Mean is the average of the given values, and the median is the central value of the given data.
 The mean value represents the average value and it may not be equal to any of the data values, and the median is equal to one of the data values.
 Adding extreme values to the data as outliers affects the mean, but it does not affect the median value.
 Mean does not require the order of the data values, as it takes the average of the data values. But the median takes into account the sequence of the values of the data and takes the middlemost value of the data as the median.
 For mean, each of the values is taken for calculation, and for the median, all the values are not taken for the calculation.
Difference Between Mean and Mode
Mean is the average of the given data points, and mode is the value of the data point which is repeating the maximum number of times. The following points help in more clearly understanding the difference between mean and the mode.
 Mean is the mathematical average, and the mode is the data with the highest frequency.
 Mean represented the average value and it may not be equal to any of the data values, but mode is the data value that is occurring the maximum number of times.
 Adding extreme values as outliers affects the value of the mean, but it does not affect the value of the mode.
 Mean does not require the frequency of occurrence of each of the data values as it only takes the average of the data, but mode requires the frequency of each of the data as it takes the data point with the highest frequency.
 For mean each of the data values is taken for calculation, and for mode, the data values are not required for calculation.
Difference Between Median and Mode
Median is the middlemost data value obtained after arranging the data in ascending or descending order. Mode is the data value that is occurring the maximum number of times or which is having the maximum frequency. The following points help in more clearly understanding the difference between median and mode.
 Median is the middlemost value of the data points and mode is the data with the highest frequency.
 Median is the middlemost value after arranging the data is the sequence of their values, and mode is the data point that is occurring the maximum number of times.
 Adding extreme values ad outliers does not affect the value of the median or the mode of the data.
 Median does not require the frequency of occurrence of the data values but it requires the data to be arranged in ascending or descending order and takes the middlemost value, and mode requires the frequency of the data as it takes the data point with the highest frequency.
 Median and mode do not require any mathematical calculations, but only require an observation of the given data values.
Related Topics
The following topics help in a better understanding of the difference between mean median and mode.
Examples on Difference Between Mean Median and Mode

Example 1: Which among the central tendencies would have the highest value for the following data points? 13, 17, 22, 37, 56, 17, 29, 34,
Solution:
The given data is 13, 17, 22, 37, 56, 17, 29, 34
Arranging this in ascending order we have 13, 17, 17, 22, 29, 34, 37, 56
Mean = (13 + 17 + 17 + 22 + 29 + 34 + 37 + 56)//8 = 225/8 = 28.12
Median = (2 + 29)/2 = 25.5
Mode = 17
Observing the above 3 values, the mean has the maximum value.
Therefore, the central tendency of mean has the highest value for this given data.

Example 2: Find the value of the median of the data, if the mean is 21 and the mode is 18.
Solution:
The given values are as follows.
Mean = 21, Mode = 18 Median = ?
The formula for mean, median, and mode is as follows.
Mode = 3 Mean  2 Median
18 = 3(21)  2 Median
18 = 63  2Median
2Median = 63  18
2Median = 45
Median = 45/2 = 22.5
Therefore, the median value is 22.5
FAQs on Difference Between Mean Median and Mode
What Is the Difference Between Mean Median and Mode?
The difference between mean median and mode is based on how it is calculated. The mean is the average of the data, the median is the middlemost value of the data arranged in a sequence, and the mode is the data that is occurring the maximum number of times. Among the three measures of central tendencies only mean involves mathematical calculation. The addition of more data as outliers affects the mean value, and less of median value and the mode value is affected.
What Is the Relationship Between Mean Median and Mode For Positive Skewness?
The relationship between mean, median, and mode for positive skewness is mean > median > mode. Here, mean is greater than median and mode, and mode is the smallest value among mean, median, and mode.
What Is the Relationship Between Mean Median and Mode?
The relationship between mean median and mode is Mode = 3Median  2Mean. Here the mode is equal to a difference of three times the median and two times the mean of the given data points.
Which Of The Three Measures of Central Tendencies of Mean Median and Mode Involve Mathematical Calculations?
Among the three measures of central tendencies of mean median and mode, the mean involves mathematical calculations. Mean is the average of the given data values, which is obtained by the sum of the given data points divided by the number of data points. Median is the middle most value of the data points after arranging the data in ascending or descending order, and mode is the data point with the highest frequency. The median and mode are the measures of central tendencies which are obtained by observing the data and does not involve any calculations.
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