# Measures of Central Tendency - example calculation explanation

Hey,
Can somebody explain the calculation behind the solution to these two examples, it makes sense visually but I’m getting confused during calculations.

I think for the 2nd example, the median might be wrong.

Given n =5 ( total 6 samples), therefore it would be the average of 2 and 3 = (2+3)/2 = 2.5

Median = 2.5, given 6 samples
I am not clear why median = 1.

Average is the weighted average (not just average) :
weighted average =
(0.1680 + 0.3601 + 0.380872 + 0.13233 + 0.028354 + 0,002435)/(0.168+0.360+0.38087+0.1323+0.02835)

weighted avg = 1.5

Mode is the biggest number: mode => 0.36, which is mode =1

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Hey thanks for the explanation, I understand the mean and mode part, but not sure how come median is 1.5, it’s supposed to be avg to middle two values in a sorted array right?
Can somebody explain the calculation of median in the 2nd example?

The median is wrong.

It should be median = 2.5. 6 Samples with x = (0,1,2,3,4,5) have to yield a median = 2.5.

There is no trick to it.

@Kevin_Shey The median in the picture is correct, for a binomial distribution the median is defined in terms of CDF, it’s the value of random variable where it’s CDF crosses 0.5.
source: My PhD mentor.
thanks for your help.