Q3 of 9 Page 249

Prove that for a set of n numbers in arithmetic sequence, the mean and median are equal.

let the first value be ‘a’ and the common difference be ‘d’.


⇒


Now we know that any kth term of the AP is given by


a + kd


n is the total number of terms, so the middle term would be .


and its value would be which is equal to the mean.


More from this chapter

All 9 →
1

The distance covered by an athlete in long jump practice are

6.10, 6.20, 6.18, 6.20, 6.25, 6.21, 6.15, 6.10


in metres. Find the mean and median. Why is it that there is not much difference between these?

 2

The table below gives the rainfall during one week of September 2015 in various districts of Kerala.


Calculate the mean and median rainfall in Kerala during this week. Why is the median less than mean?

 1

15 households in a neighbourhood are sorted a according to their monthly income in the table below.


Calculate the median income.

 2

The table below shows the workers in a factory sorted according to their daily wages:


Calculate the median daily wage