1. Averages
Objectives
Recap types of averages, and how to calculate them.
Find the mean, median and mode from frequency tables.

2. The ‘favourite’ average
Averages
Mean
Median
Mode
The ‘normal’ average
The ‘middle’ average
The ‘favourite’ average
Add them up and divide by how many there are
Put them in order and choose the middle one
The most common or most popular value

3. ½ more, ½ less Most likely
Shared out equally
½ more, ½ less
Most likely

4. There once was a woman from Dundee
Whose age had last digit three
If her whole age reversed
Is the square of the first
Then what must the woman's age be?
A Dozen, a Gross, and a Score
Plus three times the square root of four
Divided by seven
Plus five times eleven
Equals nine squared and not a bit more.

5. What length of word is the most common?
There once was a woman from Dundee
Whose age had last digit three
If her whole age reversed
Is the square of the first
Then what must the woman's age be?
Letters
Frequency 1 2 4 3 9 6 5 7 8
Mode: 3
What length of word is the most common?

6. What length of word is exactly in the middle?
There once was a woman from Dundee
Whose age had last digit three
If her whole age reversed
Is the square of the first
Then what must the woman's age be?
Median: 4
What length of word is exactly in the middle?

7. If they were shared out equally, how many letters to a word?
There once was a woman from Dundee
Whose age had last digit three
If her whole age reversed
Is the square of the first
Then what must the woman's age be?
Mean:
3.9
If they were shared out equally, how many letters to a word?

8. Mode from a Frequency Table
1) Identify the category with the largest frequency
the number of the category is the mode

9. Median from a Frequency Table
1) Complete a ‘cumulative frequency’ column
this is a running total of the frequencies
2) Determine the middle value
(total + 1) ÷ 2
3) Identify the category containing the middle value
the number of the category is the median

10. Mean from a Frequency Table
1) Complete a ‘frequency x class’ column
this gives the total of the items for each category
2) Find the total of this column, and the frequency
these are the totals needed for the mean
3) Total ‘frequency x class’ divided by total frequency
the number you calculate is the mean

11. A Dozen, a Gross, and a Score
Plus three times the square root of four
Divided by seven
Plus five times eleven
Equals nine squared and not a bit more.

12. Use suitable graphs to compare the two distributions of word lengths
Dundee
Dozen
Letters
Frequency 1 2 4 3 9 5 7 6 8
Letters
Frequency 1 4 2 3 5 7 6