Relationship between mean, median and mode

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

 

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

 

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

 

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

 

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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:

 

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

 

Solution:

 

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5 responses to Relationship between mean, median and mode

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

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