In statistics, because that a moderately it was crooked distribution, over there exists a relation in between mean, median and mode. This average median and also mode partnership is recognized as the empirical relationship” which is characterized as Mode is same to the difference between 3 time the median and 2 times the mean. This relation has been questioned in information below.

You are watching: What is the relationship among the mean, median and mode in a symmetric distribution?

To recall,

Mean is the median of the data collection which is calculation by including all the data worths together and also dividing it by the total variety of data sets.Median is the center value among the observed set of values and is calculation by arranging the values in ascending stimulate or in to decrease order and then choosing the middle value.Mode is the number from a data collection which has actually the highest frequency and is calculated by counting the variety of times each data value occurs.

Empirical Relationship in between Mean, Median and also Mode

In instance of a moderately it was crooked distribution, the difference between mean and mode is nearly equal to 3 times the difference in between the mean and also median. Thus, the empirical mean mean mode relationship is provided as:

Mean – mode = 3 (Mean – Median)


Mode = 3 average – 2 Mean

Either of these two methods of equations deserve to be provided as every the convenience because by expanding the very first representation we gain the 2nd one as presented below:

Mean – setting = 3 (Mean – Median)

Mean – setting = 3 mean – 3 Median

By rearranging the terms,

Mode = typical – 3 mean + 3 Median

Mode = 3 typical – 2 Mean

However, we can define the relation between mean, median and mode because that different varieties of distributions as defined below:

Mean median Mode Relation through Frequency Distribution

Frequency distribution with symmetrical Frequency Curve

If a frequency circulation graph has actually a symmetry frequency curve, climate mean, median and also mode will certainly be equal.


For Positively skewed Frequency Distribution

In instance of a positively it was crooked frequency distribution, the typical is always greater than median and the median is constantly greater 보다 the mode.


For Negatively it was crooked Frequency Distribution

In situation of a negatively skewed frequency distribution, the median is constantly lesser 보다 median and also the median is constantly lesser than the mode.


Also Check: Mean average Mode Formula

Example inquiry Using the Mean, Median and also Mode Relationship

Question: In a moderately it was crooked distribution, the mean is 20 and the average is 22.5. Utilizing these values, discover the approximate worth of the mode.



Mean = 22.5

Median = 20

Mode = x

Now, utilizing the relationship in between mean mode and also median us get,

(Mean – Mode) = 3 (Mean – Median)


22.5 – x = 3 (22.5 – 20)

22.5 – x = 7.5

∴ x = 15

So, setting = 15.

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For any type of given data, average is the median of offered data values and this have the right to be calculate by splitting the sum of every data values by variety of data values. Typical is the middlemost worth of the data collection when data values room arranged one of two people in ascending or diminish order. Mode is the most frequently emerged data value.
Empirical relationship in between mean median and also mode because that a moderately skewed circulation can be provided as:Mean – mode = 3 (Mean – Median)OrMode = 3 typical – 2 Mean

What is the relation in between mean median and mode for a frequency distribution with symmetrical frequency curve?

For a frequency circulation with symmetry frequency curve, the relation in between mean median and mode is offered by:Mean = median = Mode
For a positively it was crooked frequency distribution, the relation between mean median and mode is:Mean > typical > Mode