average

[Soumita Ghosh]

I have 2 questions:


I)mean and median of odd series of number are always equal??


For example:


5,6,9,10,14

Mean/average = 9 and also median=9

2) Same as equally spaced number we can the find the average/mean by following method:

(First+Last)/2

I want to know this in order to clear my concept.

[Anurag@Gurome]

I)mean and median of odd series of number are always equal?

I couldn't understand what you mean by "odd series of number".
But if you are talking about a series of number in which number of terms is odd, then NO.
For example, {1, 2, 9}. In this set median = 2 but mean = (1 + 2 + 9)/3 = 12/3 = 4

Same as equally spaced number we can the find the average/mean by following method:

(First+Last)/2

When all the elements of a set are uniformly distributed (see note) around the mean, then mean of the set = median of the set and you can use that formula. For example, {1, 2, 3, 4, 5} or {1, 2, 7, 12, 13} etc.

Note : The phrase "uniformly distributed around the mean" may create some confusion. I'm using the phrase "uniformly distributed around the mean" to mean that the first term and last term, second term and second last term, third term and third last term,... n-th term and n-th last term are equidistant from the mean. Equally spaced numbers are a special case of this scenario.

For example, the terms of {1, 2, 7, 12, 13} are not equally spaced. But the first term 1 and the last term 13 are equidistant from the mean, i.e. 7. And so are the second term 2 and the second last term 12.

However, the reverse is not true, i.e. mean of a set = median of the set doesn't imply the elements are uniformly distributed around the mean. For example, in the set {5, 6, 9, 10, 14}, mean = median but the numbers are not uniformly distributes around the mean.