# Relationship between mean, median and mode

An empirical relationship exists between mean, median and mode. For a moderately skewed distribution it is:

• If a frequency distribution has a symmetrical frequency curve, the mean, median and mode are equal.

• If a frequency distribution is positively skewed, then mean is greater than median and median is greater than mode.

• If a frequency distribution is negatively skewed, then mean is less than median and median is less than mode.

Since median always lies between mean and mode in a moderately skewed distribution, therefore it is considered as most realistic measure of central tendency.

Problem: For a moderately skewed distribution mode = 50.04, mean = 45, Find median.

Solution:

Problem: If median = 20, and Mean = 22.5 in a moderately skewed distribution then compute approximate value of mode.

Solution:

### 11 responses to Relationship between mean, median and mode

lovely says:

thanx for providing valuable information

Lalsiamkima says:

Thanks

megggy says:

its very funny

Sweety says:

Hi everyone it’s Sweety studying 10th standard I want a clear derivation of empirical relation between mean,mode, and median
Can anyone suggest a link or the website
Thank you
Sweety

Richard says:

U never described the symbols in the graph, its like they are contradicting with the statements.

kaka says:

thanks! =D

thanks for giveing a hint…

amita says:

thanks its good to understand in short time.

sayak sarkar says:

It will be so much enriched if mean,median,mode of distributions like Binomial,normal and others are added.

Zizipho says:

Thank you

Parag Gupte says:

It doesn’t always work