Question

Find the median of the first 15 odd numbers.

Answer 1

Hint: In order to solve this problem you need to write the first 15 odd numbers and the number of terms is 15 and 15 is odd so we will add one to 15 and make it even so that we can divide it by two to get the middle number. The first 15 odd numbers are 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27 and 29. Knowing this will solve your problem.

Complete step by step answer:
Median: The middle number found by ordering all data points and picking out the one in the middle (or if there are two middle numbers, taking the mean of those two numbers).
Odd numbers are those numbers which are not visible by two giving an integer every number in the form of 2n + 1 are odd if n belongs to integers.
The first 15 odd numbers are 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27 and 29.
There are 15 terms so n = 15. So, we will add 1 and divide it by 2 to get the term which is the median of the series above.
So, we will calculate the term’s place to get the value of median.
Median = $\dfrac{1}{2}\left( {n + 1} \right)$.
Here n = 15.
Median = $\dfrac{1}{2}\left( {15 + 1} \right) = \dfrac{{16}}{2} = {8^{th}}\,$ term.
So, the $8^{th}$ term of the series is 15.

Hence the median of the first 15 odd numbers is 15 as it is in the middle.

Note: When you ask to find the median of the series you just need to find the middle number in case of even number of terms there are two medians and incase of odd number of terms there are 1 median. You also need to know that Odd numbers are those numbers which are not visible by two giving an integer every number in the form of 2n + 1 are odd if n belongs to integers.