Hands-on math!

Notes on Statistics

What are statistics?

Statistics are all about things that have already happened!
Statistics are numbers that describe a set of data.

What is a set of data?

A set of data is any set of numbers that describe something. They can be grades on school tests,
temperatures in Seattle throughout the year or numbers that come up on dice that you throw.

What are some statistics?

Well, let's say we rolled 2 dice 11 times and we wrote down their totals. Here they are:

6     4     10     8     8     7     2     3     9     8     12    
The maximum is the largest number: 12
The minimum is the smallest number: 2
The range of a set of data is the maximum (highest) minus the minimum (lowest) number.
In our example, the range is: 12 - 2 = 10.

The mean is the average of all the numbers. The average of the 11 numbers in our set is:

6  +   4  +   10  +   8  +   8  +   7  +   2  +   3  +   9  +   8  +   12
    =   77
    = 7
The mode is the most common number in the set. It is the one that occurs most often.
In our set, the mode is 8 because there are 3 of them and only one each of the other numbers.

The median is the number in the middle. Here's how you find it:
If your set of data is in numerical order:
  • Odd number of elements: Find the middle one.
    For example, if you have a data set of 11 elements that are in numerical order, then the median will be the 6th element.
  • Even number of elements:
    Average the 2 middle ones.
If your data set is not in numerical order
You can use the "cross-out method":
You cross out the lowest number, then the highest number and you keep going until there is only one number left. That one will be the median.
If your data set has an even number of elements, you average the last 2 remaining elements to find the median.
As a practice, here's our dice roll data set. Find it's median by using the cross-out method:
(I'll cross out the first 2 for you!):
6     4     10     8     8     7     2     3     9     8     12    

      The median number is ___

OK, here's a problem for you: Find the mean, mode, range and median of this set of test scores:

    72     74     80     85     85     86     88     92     94 Mean = _____     Mode = _____
Range = _____    Median = _____