Mathematics

Averages

MODE AND MEDIAN

We use averages every day and averages are very useful in giving us a picture of what is going on with a lot of information.

Take for example the television programme 2.4 Children.

This is based upon an average.  It is because if you look at the number of families in the U.K. and the number of children on AVERAGE the number of children in each family is 2.4.

Notice that you can't get .4 of a child but on average this is the number.

We have different types of average

Mean

        Mode

                Median

Each has got its strengths and weaknesses. Yesterday we introduced the mean, today we are going to introduce the mode and the median.

The mode 

The Mode means the most "commonly occurring" number.

Here is a set of data (numbers) what is the mode of this set.

1, 3, 4, 5, 5, 3, 6, 2, 5, 4, 6, 5,

Answer

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

The answer is 5

Here's how it was done.

Which number in this set occurs the most?

We could rearrange these numbers to ensure that we do not miss any out.

 

So 1, 3, 4, 5, 5, 3, 6, 2, 5, 4, 6, 5, becomes 1, 2, 3, 3, 4, 4, 5, 5, 5, 5, 6, 6,

You can now see that 5 is the most common.

Hence 5 is the mode.

To revise the mean, can you find the mean of the data above?

Answer

 

 

 

 

 

 

 

 

 

 

 

 

 

The answer is 4.08 

Here's how we did it.

Add up all the numbers to find the total. 1, 2, 3, 3, 4, 4, 5, 5, 5, 5, 6, 6, = 49

And divide by the number of digits, which = 12

Hence 49/12 = 4.08. This is the mean average.

Notice how the mean and the mode are different. But they both are around the middle value.

There is one more type of average and that is the Median.

 

Median

To find the median we must always arrange the data in the order from the smallest to the largest and then find the middle value. Lets look at an example.

Here is the data

4, 6, 5, 7, 3, 2, 6. What is the median of this set of data?

 

Step 1. Rearrange the data from the smallest to the largest.

2, 3, 4, 6, 5, 6, 7

Step 2. Find the middle value 2, 3, 4, 5, 6, 6, 7

Here the middle value is 5 because there are 3 numbers on each side of it. Do you see why it is important to arrange the numbers now?

That was easy wasn't it?

Now to finish, revise the other two methods. Find the mode and the mean of the set of data we used to find the median.

Answers

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Here are the results.

Mode = 6 (because is the most common number)

Mean = 4.71 (total = 33) (number of items = 7) 33 7=4.71

Well that was easy wasn't it. We well show you some test questions on averages before the SATs so you can check your understanding further.

Till then, let's review what we have done today and yesterday.

Review

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

AVERAGES REVIEW

There are three types of average.

Mean

Mode

Median

 

Mean

To calculate the mean, we add up all the numbers to find the total number (the sum) and divide by the number of events.

Mode

The mode is the most common number in the data range.

Median

We find the median by arranging the data in order then finding the middle value

Don't forget the range, this from the lowest to the highest number.

Finally remember the average is ALWAYS in the middle of a set of numbers

Good luck!

 

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