Question

A data set has a median of 2320, and eight of the numbers in the data set are less than 2320 . The data set contains a total of n numbers.

If n is even, and none of the numbers in the data set are equal to 2320 , what is the value of n?

Answer 1

n = 16

Explanation:

median = 2320

n is even, so the median is the mean of the two middle numbers.

Let x and y be the two middle numbers, with y > x.

The median is 2320, and the number of numbers is even, so the median is (x + y)/2. Since x and y are not equal to 2320, then x < 2320, and y > 2302.

There must be 7 more numbers less than 2320, so you have:

a, b, c, d, e, f, g, x, y, i, j, k, l, m, n, o

The total number of numbers is 16.

n = 16