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 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 1

2 4

3 9

4 6

5 7

6 3

7 0

8 1

Mode:

3

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

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

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) ÷ 23) 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 frequencythe 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

Letters Frequency

1 4

2 2

3 5

4 7

5 7

6 3

7 2

Letters Frequency

1 1

2 4

3 9

4 5

5 7

6 3

7 0

8 1

Dundee Dozen