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

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

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

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.

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?

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?

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?

Mode from a Frequency Table 1) Identify the category with the largest frequency the category itself is the mode

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 category itself is the median

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) Divide total ‘frequency x class’ by total frequency the number you calculate is the mean

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. Joint mode: 4 and 5 Median: 4 Mean: 3.93333...

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