Topic outline
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In this course you will learn about:
- Collecting data.
- Summarising data.
- Representing data.
- Interpreting data.
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Why do we collect data?
Data are a collection of unorganised observations and can contain thousands of entries. We collect data to gain information and solve a problem or make informed decisions. In order to make sense of the data we need to condense it or organise it in a way that makes interpretation easier.
Data is used to calculate statistics, which help you understand what the data collected is all about. Data collection is very important for many businesses to make sure they are operating optimally.
Before you learn about organising, representing and summarising data, it is important that you understand the different types of data.
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Types of data
Data are either qualitative or quantitative. This description can be further divided into continuous, discrete, grouped or ungrouped data. The different forms of data are explained in the following video. After you have watched the video try the activity that follows.
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To make sense of data we need to condense it or organise it in a way that makes interpretation easier. The method used to condense or summarise the data depends on whether data are grouped or un-grouped. Remember that ungrouped data is unorganised or raw data. And, grouped data has been organised in some way.
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Frequency distribution
Before you summarise data, it is important to understand how to organise data using frequency distributions. By counting how often data values appear we can make a frequency distribution. The next video gives an example of how to organise data using a frequency distribution also called a frequency table.
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Cumulative frequencies
Some graphs that represent data from a grouped frequency distribution need cumulative frequencies. Cumulative means to add up or collect values together.
You can think of cumulative frequency as the running total of frequencies in a frequency distribution. This means you are adding a value to all of the values that came before it.
To find the cumulative frequencies, add all the previous frequencies to the frequency for the current row, as shown in the table.
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Measures of central tendency
We gain a better understanding of data by summarising it numerically using statistics. Two types of summary measures that are used are; measures of central tendency (averages) and measures of dispersion (spread).
You can read more about summarising data in: Revise measures of central tendency.
You can watch the next video for an introduction to averages.
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Calculate averages
Try the next exercise to see if you understand how to calculate the mean, median and mode.
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Measures of dispersion
The measures of central tendency do not fully describe a data set and can often be misleading if we do not know how spread out or variable the data are. To work out the variation in data we have to calculate measures of dispersion.
You can discover more about variation in data by going through the exercises in: Measures of dispersion.
The following video takes a closer look at how to calculate the interquartile range.
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Calculate measures of dispersion
The next 2 exercises will test your ability to calculate the range and interquartile range.
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It is easier to get information by looking at a representation of data rather than working through the data in a frequency table. Data may be represented using:
- Line graphs
- Bar graphs
- Histograms
- Pie charts
- Frequency polygons or
- Ogives.
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Line graph
Line graphs are used to show trends in data. The next video explains this in more detail.
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Bar graph
Generally bar graphs are used for comparison of discrete non-numerical (qualitative) data and cannot be used to represent continuous data. Bar graphs must have distinct gaps between the bars.
In the next video you will use an example to learn how to draw a bar graph.
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Pie chart
Pie charts are easy to identify because they look like circle graphs. A pie chart is used to show the relative sizes of different pieces of data that make up a whole survey or observation.
You can learn more about drawing pie charts in this textbook: Creating Pie Charts. Remember to watch the video contained in the text so you can also see how pie charts are constructed.
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Histogram
A histogram is usually drawn to display continuous data hence the bars do touch. In the next video you will learn about constructing histograms and when to use this graph.
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Frequency Polygon
A frequency polygon can be drawn directly from a histogram. Frequency polygons are generally used to compare sets of data.
The method of constructing a frequency polygon is discussed in: Frequency Polygons. Click on the link and watch the video to learn the steps for drawing a frequency polygon.
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Ogive
An ogive (pronounced oh-jive) is also called a cumulative frequency graph. It is used to represent cumulative frequencies and to estimate the number of data observations that are less than or equal to a certain value.
The steps for constructing an ogive are discussed in: Cumulative Frequency Distribution.
You can practise all the ways that you learnt to represent data in the next activity.
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Practise representing data
Here are a few activities to help you practise drawing the different types of data graphs. Click on each one and work through the questions to test your knowledge.
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Data can be manipulated and changed to misrepresent the facts and give an incorrect picture of the truth. So, you need to analyse and interpret the data you are shown carefully.
The next video explains how data representations can be misleading.
One of the main goals of collecting data is to be able to interpret the results and make conclusions or decisions. You can learn more about using data to make accurate decisions in: Interpreting data.