averages objectives recap types of averages, and how to calculate them. find the mean, median and...
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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
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