Determine the mean, median, and mode for the given data. Anthony is 18 years old, Noah is nine, Olivia is 15, Liam is 18, Matthew is 10, Natalie is seven, Amelia is 14, and James is five.
The mean is the average. The median will be the middle number and the mode will be the number that occurs most often. And these numbers we’re talking about are the ages. So to find the average, we need to add them all up and divide by the number of ages they actually are.
So again, to find the average, the mean, we should add all of the ages up and then divide by the number of the ages. And how many ages are there? There are eight. So let’s add all the ages together on the numerator. And we get 96 and 96 divided by eight is 12. So the average age for this set of data is 12 years old.
Now, in order to find the median, the middle number, we must first list the ages from youngest to oldest. James is the youngest and he’s five, then Natalie who’s seven, then Noah who’s nine, then Matthew who’s 10, then Amelia who’s 14, Olivia who’s 15, and then Anthony and Liam are both 18.
So to find the median, the middle number, we need to find the middle number itself. So how many numbers are there? Well, we know that there are eight ages. So there must be eight numbers. So what number would be in the middle of eight? Well, half of eight is four. So half of the data is five, seven, nine, 10 and half of the data is 14, 15, 18, and 18.
So to find the middle, we need to find the middle number between 10 and 14, which is 12. Therefore, the median would be 12. 12 is in between 10 and 14 because it’s two away from 10 and two away from 14.
Now, for the mode, what number occurs the most often? It’s helpful to list these in least to greatest order again that way we can see the repetition. And the number that occurs the most often is 18. It occurs twice. So 18 is the mode.
Therefore, once again, the mean is 12, the median is 12, and the mode is 18.