Mean, Median, Mode and Range

Median

The median is the middle number in a set of numbers.

How to remember: Median sounds like medium, which both mean in the middle.

Common mistake: Make sure that you arrange the numbers in order from lowest to highest, before finding the middle number.

• Example of common mistake:    10, 15, 23, 10, 23, 14, 17
  
• Example of correct median:        10, 10, 14, 15, 17, 23, 23

Mean

The mean is an average.

How to remember: The mean is the mean one. It requires you to add all of the numbers and then divide the sum by however many numbers there are. It is mean because it makes you do much more work than the other problems on this page.

Common Mistake: The most common mistake is to make an error adding or dividing (many students attempt to add the numbers in their heads).

Example: 10, 8, 21, 15, 12, 15
You add all the numbers together to get a total of 81. You then divide 81 by 6, which is how many numbers there are. The mean is 13.5 (We don't use remainders in 5th grade).

Mode

The mode is the most common number in a set of data.

How to remember: Mode starts the same as most, and the mode is the most common number.

Example: 10, 23, 28, 10, 24, 23, 10
Ten is the mode in this set of data, because it occurs three times.

Range

The range is the difference between the highest and lowest numbers in a set of data.

How to remember: Mean, median and mode all start with "m" but range is different, it starts with "r." You must find the difference between the highest and lowest number for the different one.

Example: 80, 90, 95, 75, 89, 72
You must subtract 72, the lowest number, from 90, the highest number, to find a range of 18.

Challenge Problem

The most difficult type of problem students will see on this standard, is listed below.

Example: Create a list of 5 numbers whose mean is 12. You must use at least 3 different numbers.

Easiest solution: Create a line plot graph and simply balance the numbers out.  If you want an average of 12, then you might have a an 11 and 13, because they will balance out at 12. You might also have a 10 and 14, because they too will balance out at 12.

Another Solution: If you need 5 numbers with an average of 12, then simply multiply 12x5 and you will know that the sum of all your numbers must equal 60. You might then choose to have a 20, 10, 5, 15, 10. This set of numbers will add up to 60, so they will have an average of 12.

Here is an example of a balanced line plot graph, as described in the easiest solution. The mean of this graph is 5, because the 4 and the 6 balance out.