Question

I saw a formula that:
Mean-Mode=3 (Mean-Median)
Lets take the data to be:
12,12,20,24,36,40
Mean=144/6=24
Mode=12
So by the formula median should be 20.
But the median in this data is
(n/2th observations+n/2+1th obs)/2.
So is the formula wrong??

Answer 1

Mean-mode=3(Mean-median)

=24-12=3(24-m)

=12=72-3m

3m=60

m=60/3

=20

So the median came to be 20.

If you use the formula (n/2+n/2+1th observation)/2 then the median will come :

20+24/2=44/2=22

But median is coming 20

The formula for median is not applicable.

Remember when graphical method comes we use n/2 th observation.

So n/2 th observation =6/2=3rd one.

Median =20

Hence use this formula n./2th observation and verify it .

The formula n/2 th+n/2+1th obs is used for measuring central tendency accurately, but in graphical method the actual formula is n/2 th.

Hope it helped.