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AveragesThere are different averages: some are more meaningful than others depending on the context.
What is the average number of ears in the world human population?
The mode (the “modal average”)
The median
The mean
The mode represents the most common value.
Modal number of ears: 2?
Median number of ears: 2?
?
The median represents the middle value.?
The mean takes into account all values. We add up the values and divide by the number of values.
Mean number of ears: 1.99999?
Averages
The mode (the “modal average”)
The median
The mean
The mode tends to be a good average when we want to give an indication of the value that is most common.
Median is often good because it makes it easier to tell whether a value is in the top 50% or the bottom 50%.It’s also less sensitive to extreme values.
The mean is the best average to use if we want to take all the values into account.
There are different averages: some are more meaningful than others depending on the context.
Salaries of people in the room: £13,000 £18,000 £24,000 £25,500 £26,000 £32,000 £45,000 £1,200,000
What would the best average be here?
AveragesCopy these numbers down, and work out the mean, mode and median.
10, 13, 15, 16, 17, 17, 20
The mode (the “modal average”)
The median
The mean 10 + 13 + 15 + 16 + 17 + 17 + 207 = 15.43?
16?
17?
Averages – Round 2!Copy these numbers down, and work out the mean, mode and median.
13, 13, 17, 20
The mode (the “modal average”)
The median
The mean
15?
13?
The range
15.75
7
?
?The range is the difference between the smallest and largest number.
When there’s two items in the middle, we use the value in between: i.e. add them and divide by 2.
In pairs, see how many of these puzzles you can work out…
The mean average of Dr Frost and Sebastian’s age is 19.5. If Sebastian is 13, how old is Dr Frost?
Answer: 26?
If the range of two numbers is 6 and the their mean is 15, what are the two numbers?
Answer: 12 and 18?
The mode of four numbers is 5. The median is 6.5 and the mean is 7. What is the range?
Answer: 7 (The numbers are 5, 5, 6, 12)
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The mean of the four numbers is 8. What is the missing number?
3 4 5 ?
Answer: 20?
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Puzzles involving the mean
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3 4
Worksheet provided!
Exercises
Age of Dog 10 11 12 13 14
Frequency 3 4 7 6 1
The “frequency” tells us how “frequent” the age of 10 is, i.e. how many times it appears.
𝑀𝑒𝑎𝑛=¿?
Mean of Frequency Tables
Bro Tip: Imagine if we actually listed out the values – how would we find the mean?
Cost £1.50 £1.65 £1.70 £1.80 £2.00
Frequency 1 20 21 5 2
Mean cost of beefburger horseburger:
= = £1.70£83.2049
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Your Go...
Weight 2kg 3kg 4kg 5kg 6kg
Frequency 4 0 8 7 3
Mean weight of cats:
= = 4.23kg9322
?
Time (secs) Frequency
Mean of Grouped Data
A number of members of 8IW are running in a race.Their times were as follows
Estimate of mean: ?
Why is it an estimate? Because we don’t know the exact times within each group.?
Age of rock (years) Frequency
Test Your Understanding
𝐸𝑠𝑡𝑖𝑚𝑎𝑡𝑒𝑜𝑓 𝑚𝑒𝑎𝑛=1150069
=166.7 𝑦𝑒𝑎𝑟𝑠
Weight of horse (kg)
Frequency
𝐸𝑠𝑡𝑖𝑚𝑎𝑡𝑒𝑜𝑓 𝑚𝑒𝑎𝑛=32165229
=140.5𝑘𝑔
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Sam collects the weights of 15 squirrels and puts them into weight ranges. His data is presented below. Estimate the mean weight of a squirrel.
Miss Clarke values a number of pieces of artwork in the Tiffin School Vault. The price ranges are summarised below. Estimate the average value of a piece of art in school.
£5119.05
I record the times of 50 runners in a 10km race. Their times are summarised below. Determine their mean time in minutes.
44.85 minutes
Exercises(Provided on printed sheet)
At a party, thirty people have an age of 30, forty have an age of 40 and fifty an age of fifty. What is their average age?
In a hardware shop, there are 30 spanners costing £6, 55 hacksaws costing £9 and 10 soldering irons costings £20. What is the average cost per item?
Using this frequency table, find the average height of a turnip.
Height (nearest cm) 6cm 7cm 8cm 9cm 10cmFrequency 3 8 12 4 1
Weight 10-16kg 16-20kg 20-30kg 30kg-32kgFrequency 7 3 4 1
Value £0-£1000 £1 000-5 000 £5 000-£20 000 £20 000-£100 000Frequency 10 25 6 1
Time (minutes) 35-40 40-42 42-48 48-60Frequency 5 15 20 10
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Exercises
I visit the lost island of Laurie and collect the weights of Kenneybirds. There are 5 birds with a weight of to and 5 birds with a weight between and . The estimate of the mean is . Determine .
I travel back in time and collect the heights of a number of Damonsaurus. There are dinosaurs with a height between 5-7km and 4 dinosaurs with heights between 7-11km. The estimate of the mean height is . How many Damonsaurus are there in total?
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