1 Mode, median, mean and range

1
SUMMARY OF WORK COVERED SO FAR
1)   Mode, median, mean and range 2)  
Pictograms 3)   Bar-charts 4)   Bar-graphs 5)  
Tally charts 6)   Grouped Data and bar
charts 7)   Frequency polygons 8)   Data in
Tables 9)   Pie charts  
2
Mode, Median and Range

• Aim
• To find the mode, median and range, and the modal
  class for grouped data.

3

• Put these numbers in numerical order with the
  smallest first.

7, 3, 9, 2, 10, 8, 5, 4, 14, 12
2,
3,
4,
5,
7,
8,
9,
10,
12,
14,
34, 67, 38, 19, 44, 57, 24, 31, 62, 20
19, 20, 24, 31, 34, 38, 44, 57, 62, 67
4

• 2, -3, 1, 4, -4, 0, 5, -2

-5
1
-4
-3
-2
0
2
4
5
5
Averages(mean)
An average is a useful statistic because it
represents a whole set of values by just a single
or typical value.

• Where have you heard the word average before?
• Where have you seen it used?

6
The Mode

• The mode is a type of average
• The mode is the value that occurs most often in
  a set of data
• Example

5, 6, 8, 2, 4, 5, 3, 5
MODE 5
Sometimes there is no mode because either all the
values are different, or no single value occurs
more often than other values
7
W
THE MODE DOESNT HAVE TO BE A NUMBER

• What letter does your first name begin with?

T
F
H
What is the mode first letter for a name in class
7Y2?
P
8
The Median

• The median is another type of average
• The median is the middle value for a set of data
  when the values are put in numerical order.

Example
6, 8, 3, 7, 5, 2, 4 in order
2, 3, 4, 5, 6, 7, 8
Median 5
For an odd number of values in data set, there is
only one middle value. This is the median.
9
What is the median test score for the following
set of results?
5, 7, 7, 8, 10, 12, 14, 15
Median 9
For an even number of values in a data set, there
are two middle values.
The median is the value in the middle of these
two values.
10
The Range

• The range is not an average.
• The range of a set of data is the largest value
  minus the smallest value.
• It shows how the data is spread out.

A small range shows
that the values in a set of data are similar in
size
A large range shows
that the values differ considerably
11
Find the range
What number month were you born in?
For example, January 1, June 6, and December
12
Range Largest number smallest number
Range
What does this tell us about the birthdays of
class 7Y2?
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Modal Class
For grouped data such as the example below, we
cannot find the mode.
Modal class 3-5
Instead, we find the MODAL CLASS. This is the
group that occurs most often.
Why isnt it possible to calculate an exact mode
or median from grouped data?
13
Write down
5 numbers with a mode of 7
7 numbers with a median of 3
7 numbers with a mode of 6 and a median of 12
7 numbers with a mode of 5, median of 8, and a
range of 10
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Pie Charts

• Be able to construct a pie chart from a
  collection of data, using a protractor.

15
Makes of car in a school car park
Construct a pie chart to show this information. A
full circle is 360o There are a total of 3241
10 cars We use 36o to represent each car
360o
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Work out the missing numbers on this number spider
12
90
30
30
4
12
360
4
15
90
24
20
15
18
24
10
36
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Makes of car in a school car park
3x36o108o
2x36o72o
4x36o144o
1x36o36o
We use 36o to represent each car so the3
Cavaliers are represented by 3x36o 108o Work
out the angle needed for each of the other models
of car
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Makes of car in a school car park
Mark the centre of the pie and draw the
circle. Draw a line from the centre to the
edge Measure the first angle needed (108o) Draw
in the line and label the section
Cavalier
108o
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Makes of car in a school car park
From this line measure the next angle, draw the
line and label the section. Continue in this
way Check that the last section has the correct
angle and label it.
Volvo
36o
Cavalier
Rover
144o
72o
Ford
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Why?

• Why do we use 36o to represent 1 car?
• What would happen if there were 20 cars?
• What about 60 cars? Or 15 cars?
• If there were 20 cars in your survey, what angle
  would you use to represent 4 cars? 7 cars? 12
  cars?

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Construct Pie charts questions

• Q1 A survey of how 30 pupils got to school
• Q2 How Cameroon spent his 40 birthday money
• Q3 Who is your favourite Telly-Tubby survey.

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Interpreting Pie Charts

• 20 pupils in class 3B travel to school. From the
  chart find the number of pupils who travel by
  each method.
• Walk
• Cycle
• Bus

23
180 boys in year 5 chose their favourite sport.
From the chart find how many chose each sport.
24
300 passengers boarded a train in London. From
the chart find how many are travelling to each
destination.
25
150 packets of crisps were sold from a vending
machine. From the chart find the number for each
flavour. Find also the percentage for each.
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Answers
SportsFootball 72, Rugby 40, Hockey 30Cross
Country 20, Squash 18 pupils. Passengers
Southampton 100, Bournemouth 75, Poole 50,
Branksome 45, Parkstone 30. Crisps Plain 60,
Cheese Onion 45,Salt Vinegar 30, Prawn
Cocktail 15