Last modified 12 th October 2013 Averages There 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 ID: 703017
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Slide1
KS3 Mean, Mode, Range
Dr J Frost (jfrost@tiffin.kingston.sch.uk)
Last modified: 12
th
October 2013Slide2
Averages
There 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
?Slide3
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?Slide4
Averages
Copy 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 + 20
7
= 15.43
?
16
?
17
?Slide5
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.Slide6
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)
?
The mean of the four numbers is 8. What is the missing number?
3
4
5
?
Answer: 20
?
1
Puzzles involving the mean
2
3
4Slide7
Worksheet provided!
ExercisesSlide8
KS3 Mean of Frequency Tables
Dr J Frost (jfrost@tiffin.kingston.sch.uk)
Last modified:
22
nd
November 2013Slide9
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 of Frequency Tables
Bro Tip:
Imagine if we actually listed out the values – how would we find the mean?Slide10
Cost
£1.50
£1.65£1.70£1.80
£2.00Frequency120
21
5
2
Mean cost of
beefburger
horseburger: = = £1.70
£83.2049
?
Your Go...
Weight
2kg
3kg
4kg
5kg
6kg
Frequency
4
0873
Mean weight of cats:= = 4.23kg
9322
?Slide11
Time (
secs
)Frequency
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.
?Slide12
Age of rock
(years)
Frequency
Age of rock
(years)
Frequency
Test Your Understanding
Weight of horse (kg)
Frequency
Weight of horse (kg)
Frequency
?
?Slide13
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
10cm
Frequency
3
8
12
4
1
Weight
10-16kg
16-20kg
20-30kg
30kg-32kg
Frequency
7
3
4
1
Value
£0-£1000
£1 000-5 000
£5 000-£20 000
£20 000-£
100
000
Frequency
10
25
6
1
Time (minutes)
35-40
40-42
42-48
48-60
Frequency
5
15
20
10
?
?
?
?
?
?
1
2
3
4
5
6Slide14
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
?
?
?
6
7