Mean puzzles

Hello, and welcome to Myriora Maths! Three friends have a mean score of eight. Two of them scored six and nine. What did the third friend score? Let's crack mean puzzles!

The key is the total. If three scores have a mean of eight, they add up to three times eight: twenty-four.

Six add nine is fifteen. So the third score must be twenty-four take away fifteen: nine.

Now a fourth friend joins, with a score of twelve. The new total is twenty-four add twelve: thirty-six. Shared between four: the new mean is nine.

The mean went up, because the new score was bigger than the old mean. A score smaller than the mean would pull it down.

Let's try one together. Two numbers have a mean of five. What do they add up to? Say it out loud!

Two times five: they add up to ten!

Here's a question that catches lots of people. The mean of three scores is eight. Two are six and nine. Some people take the mean of six and nine, and say seven and a half. But you need the total! Three times eight is twenty-four, so the missing score is nine.

Your turn! Four numbers have a mean of five. Three of them are two, four and six. What is the fourth? Pick the right card. You've got twenty seconds, or pause the video. Go!

Time's up! The total is four times five: twenty. Two add four add six is twelve. Twenty take away twelve is eight!

Quick review. To work backwards from a mean, find the total: the mean times how many. Take away the numbers you know to find the missing one. When a new number joins, find the new total, and share again. See you next time!