Averages

Objectives• Recap types of averages, and how to

calculate them.• Find the mean, median and mode from

frequency tables.

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

Shared out Shared out equallyequally

½ more, ½ more, ½ less½ less

Most Most likelylikely

There once was a woman from DundeeWhose age had last digit threeIf her whole age reversedIs the square of the firstThen what must the woman's age be?

A Dozen, a Gross, and a ScorePlus three times the square root of fourDivided by sevenPlus five times elevenEquals nine squared and not a bit more.

What length of word is the most

common?

There once was a woman from DundeeWhose age had last digit threeIf her whole age reversedIs the square of the firstThen what must the woman's age be?

Letters Frequency1 12 43 94 65 76 37 08 1

Mode:

3

What length of word is exactly in

the middle?

There once was a woman from DundeeWhose age had last digit threeIf her whole age reversedIs the square of the firstThen what must the woman's age be?

Median:

4

If they were shared out equally, how many letters to a

word?

There once was a woman from DundeeWhose age had last digit threeIf her whole age reversedIs the square of the firstThen what must the woman's age be?

Mean:

3.9

Mode from a Frequency Table

1) Identify the category with the largest frequencythe category itself is the mode

Median from a Frequency Table

1) Complete a ‘cumulative frequency’ columnthis is a running total of the frequencies

2) Determine the middle value(total + 1) ÷ 2

3) Identify the category containing the middle valuethe category itself is the median

Mean from a Frequency Table

1) Complete a ‘frequency x class’ columnthis gives the total of the items for each category

2) Find the total of this column, and the frequencythese are the totals needed for the mean

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

A Dozen, a Gross, and a ScorePlus three times the square root of fourDivided by sevenPlus five times elevenEquals 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

Letters Frequency1 42 23 54 75 76 37 2

Letters Frequency1 12 43 94 55 76 37 08 1

Dundee Dozen