Name:______________________________
HANDLING DATA
Bar charts
Bar charts are one way of showing the information from a
frequency table. This bar chart represents the data from the
table on the previous page:
The heights of the bars in this bar chart show how many of
each bike were sold.
Pictograms
Pictograms are another way of showing the information
from a frequency table.
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The key shows that 2 bikes are represented by a picture of a
wheel. So half a wheel must represent 1 bike.
Pie charts
Pie charts are circles divided into segments, where each
segment represents a fraction of the total amount.
This pie chart shows the 20 bikes sold at the bike shop. The
segment for Mountain bikes is one half of the chart. This is
because 10 Mountain bikes were sold, which is exactly half
the number of bikes sold in total (20 bikes).
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Line graphs
A line graph is used to plot a set of data over an amount of
time. This line graph plots the temperature of a hot drink
over an hour. You can see how the drink temperature cools
over time:
Always look carefully at the scale on each axis of the graph each mark represents a different number.
To find the temperature of the drink after 20 minutes:
. Find the 20 minutes mark along the bottom axis of the
graph.
. With a ruler or your finger, follow the line upwards until
you reach the curved graph line.
. Now follow the line to the left until you reach the vertical
axis.
. You can now read the temperature of the graph and find
out that the drink was 40°C after 20 minutes.
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Mode, median and mean
Mode, median and mean are three different types of
average. Let's work out the mode, median and mean of this
set of numbers:
7 9 11 6 13 6 6 3 11
Mode
The mode is the value that appears the most.
To work out the mode:
. Put the numbers in order:
3 6 6 6 7 9 11 11 13
Look for the number that appears the most.
6 appears more
than any other number.
So the mode value is 6.
Median
The median is the middle value.
To work out the median:
. Put the numbers in order:
3 6 6 6 7 9 11 11 13
. The number in the middle of the list is the median.
So the
median value is 7.
If there are two middle values, the median is halfway
between them. Work out the median for this set of numbers:
3 6 6 6 7 8 9 11 11 13
There are two middle values, 7 and 8.
The median is
halfway between 7 and 8, so the median is 7.5.
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Mean
The mean average is not always a whole number.
The mean is the total of the numbers divided by how many
numbers there are.
To work out the mean:
. Add up all the numbers.
7 + 9 + 11 + 6 + 13 + 6 + 6 + 3 +
11 = 72
. Divide the answer by how many numbers there are.
There
are 9 numbers.
72 ÷ 9 = 8
So the mean value is 8.
Range
The range is the difference between the biggest and the
smallest number.
To work out the range:
. Put the numbers in order:
3 6 6 6 7 9 11 11 13
. Subtract the smallest number from the biggest
number:
13 - 3 = 10
So the range of this set of
numbers is 10.
What is probability?
Probability or chance is how likely something is to happen:
.
If something has a low probability, it is unlikely
to happen.
If something has a high probability, it is likely to
happen.
How to express probability
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There are two main methods of expressing probability:
. Probabilities are most commonly shown as fractions:
The probability of getting 'tails' when you
toss a coin is a 1 in 2 chance, or 1/2
The probability of getting a 3 when you roll a
dice is a 1 in 6 chance, or 1/6
. Probabilities can also be shown as decimals or
percentages:
A probability of 1/2 can also be shown as 0.5
or 50%
A probability of 3/4 can also be shown as
0.75 or 75%
The results of an experiment can give different probabilities
to those you expect. If you throw a dice six times, you would
expect to get a 6 once as the probability of throwing a 6 is 1
in 6. But in fact you might get more than one 6 or no 6s at all!
Probability scales
Probabilities can be shown on a scale between 0
(impossible) and 1 (certain).
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For example, imagine a shopping bag contains three bananas
and nothing else:
.
The probability of reaching into the bag and
pulling out a banana is 1 (certain), as there is nothing
else in the bag.
The probability of reaching into the bag and pulling out
an apple is 0 (impossible), as there are no apples in the bag.
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