Question

The mean, median, and unique mode of the positive integers 3, 4, 5, 6, 6, 7, and xare all equal. What is the value of x

Answer 1

Given :

Positive integers 3, 4, 5, 6, 6, 7, and x are all equal.

To Find :

The mean, median, and unique mode are all equal , find x.

Solution :

$mean = \dfrac{3+4+5+6+6+7+x}{7}$

Median is the middle number in sorted list.

So, median = 6

Also, mode is the number with highest frequency.

mode = 6

So,

mean = mode = median

$\dfrac{31+x}{7}=6=6\\\\x = 11$

Hence, this is the required solution.