Question

For a set of odd number of positive integers, the mean and the median are same at 18, with no mode. After adding an additional positive integer to the set, the mean, the median and the mode have become the same. What is the new integer added to the set?

Answer 1

18

Explanation:

We are not told how many numbers of odd positive integers are in the data set,

Let the number of the odd positive integers in the data set = n

For n number of odd positive integers, the mode= 0; and the mean and median = 18

The mean = 18

Mean = (sum of values)/(number of values in a data set)

Since Sum of values is unknown, let S represent it.

Mean = S/n

18 = S/n

S = 18n

the median = 18

For odd positive integers, we would have only one middle number = 18

When an additional positive integer is added to the set, the mean, the median and the mode = 18

After adding another positive integer, the data set is now even.

For a even data set, the median would have two same numbers.

From the question, the initial median was 18 and the new median is 18.

Median of the new data set = (addition of the two middle numbers)/2

Let x represent the two middle numbers

Median = (x+x)/2

18 = 2x/2

18 = x

Since the middle numbers are equal,

The new integer added to the set is 18