Mean = median

Probability Level 3

Add a fifth number $x$ to the set $\{3,7,9,10\}$ so the mean of the new set equals its median.

Enter the sum of all possible values of $x.$

The answer is 29.25.

1 solution

Jeremy Galvagni
Apr 25, 2018

The sum of the set will be $29+x$

If $x$ is smaller than 7 the median will be 7 and so the sum must be $5*7=35$ . $x=6$

If $x$ is greater than 9 the median will be 9 and so the sum must be $5*9=45$ . $x=16$

If $x$ is between 7 and 9, then $n$ itself is the median and so the sum must be $5*x$ .

Solving $29+x=5x$ gives $x=7.25$

The sum of these is $6+16+7.25=\boxed{29.25}$

Darn my brain filled in that n should b an integer... But that's bogus, cause it's just a number n that's needed.

Peter van der Linden - 3 years, 1 month ago

Good point, actually. I should change n to x. Since the former is often used to denote an integer, which is not my intention. I thought it would be more interesting if one the middle case were not a whole number.

Jeremy Galvagni - 3 years, 1 month ago

Mean = median

The answer is 29.25.

1 solution

0 pending reports