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Representing Data

Discrete Data; These are results gathered by counting things in whole numbers

Eg the different colours of cars that were cleaned in a car wash in one day

When we gather the information we would probably use a table using tally charts to count

Lets see the results from ‘Dave’s Car Wash’ on Sunday

Dave’s Sunday Car Wash

YellowCars

GreenCars

RedCars

BlueCars

BlackCars

WhiteCars

This data is in a table so it might be said to be in tabulated form

And it is sometimes known as a ‘frequency table’ or ‘Tally chart’

Dave’s Sunday Car Wash

YellowCars

GreenCars

RedCars

BlueCars

BlackCars

WhiteCars

10 10 5 10 5 20

This data is in a table so it might be said to be in tabulated form

And it is sometimes known as a ‘frequency table’

Information from tables

• Tables are a good way to record data in a tidy way, but looking at a list of numbers does not really help us to see any relationships in those numbers

• Sometimes it might be better to show a pie chart so that we can see what part of the total count each result provides

Data represented in pie charts

• It is sometimes easier to calculate what fraction of the whole count can be given to each result. If this is the fraction of a circle, then the result can be shown on a pie chart.

• In our example 20 out of sixty cars were white so 20/60 or 1/3 were white

• Now 1/3 x 360 degrees= 120 degrees

A pie chart showing cars at Dave’s car wash

x

White Cars

Blue cars

Yellow CarsGreen Cars

Black cars

Red cars

A Bar Chart Showing Dave’s Car Wash

Colour

Count

WhiteBlackBlueRedGreenYellow

20

15

10

5

0

Chart of Count vs Colour

Using the information

• From Dave’s car wash we cannot see anything very special about the data

• Perhaps only that white seems to be twice as popular than any other colour (this is shown by the largest slice in the pie chart and the highest bar in the bar graph)

• Could we say the modal colour is white?

Continuous Data

• We have so far talked about counting things and displaying this discrete data on Pie charts or Bar charts.

• If the data can take any value, say when measuring temperature or time, this is called Continuous Data

Recording Continuous data

• Some readings of volume of water in a filling bath are shown below, along with the time when that reading was taken

Time/secs

30 60 90 120 150 180 210 240

Volume/m^3

0.1 0.15

0.45 0.75 0.9 0.95

0.95

0.95

Volume of water in a filling bath

Time/ seconds

Volu

me o

f w

ate

r/m̂

3

250200150100500

1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

Volume v's time

What can we see from the graph?

• The bath starts filling very slowly for the first minute

• The rate of filling then increases sharply

• The bath is very nearly full at t=?• What is the rate of filling at 120

seconds?