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Statistics 3. Continuous data. Collecting continuous data (measured data, few values the same.) We collect data using tally charts when we want to group data into categories or stem and leaf plots when we want to have a record of each data value. Oyster length data tally chart.
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Continuous data • Collecting continuous data (measured data, few values the same.) • We collect data using tally charts when we want to group data into categories • or stem and leaf plots when we want to have a record of each data value.
Oyster length data tally chart 150 - 160 means all data that is 150 mm up to 160 mm (but not including 160 mm) The best graph to show this data is a histogram.
Histogram • Note that we always put units on the axes. • There are no gaps between bars as the data is continuous.
Histogram • The graph shows us that we have some outliers. • Most of the lengths are between 190 and 240 mm. • The modal interval is 200mm to 210 mm.
Stem and Leaf Plot 15 9 16 • 0 18 • 0 3 4 5 7 7 8 • 1 3 3 3 5 6 7 7 8 8 • 7 • 2 4 7 8 8 9 • 0 3 4 24 25 26 27 28 29 30 31 8 It looks a lot like the histogram just on its side.
Stem and Leaf Plot 15 9 16 • 0 18 • 0 3 4 5 7 7 8 • 1 3 3 3 5 6 7 7 8 8 • 7 • 2 4 7 8 8 9 • 0 3 4 24 25 26 27 28 29 30 31 8 We can get the same information from this plot as we can from the histogram.
Line graphs • Line graphs are used to show some kind of change or distinction between data.
Example • We could look at the pre-test and post-test scores of a class to gauge if there has been a change.
This gives us a picture of what happened. • Another way to show this would have been to draw a box and whisker plot.
Note that the LQ and Median were the same value • The box and whisker plots give us a clear indication that there has been a change but they don’t show us that there were 25 marks in the first test and only 17 recorded in the second and hence we cannot be certain of the conclusions that we make.
Paying our bills • Media often talk about people receiving a percentage increase in their wages. • Is this a fair way to look at things when everyone pays the same amount for goods?
Example • Mr Jones gets $381 a week. He spends $108 on food for his family of four. • Mrs Smith gets $684 a week. She spends $146 on food for her family of four. • The best way to show this situation is to draw 2 pie graphs.
Although Mrs Smith spends more on food, the percentage of her income is less.
Misleading Graphs • The impression we get is that this company is improving quite dramatically. • Notice where the y-axis begins
Misleading Graphs • Using ‘0’ as a starter value gives us a more honest representation of the data and we now see that the increase is less dramatic.
Misleading graphs • The principal of school B says her school is the most successful. • Do you agree?
Misleading graphs • We need more information to make a judgement.
Comparing graphs We now think that C is the best school because the pass rate is better.
You now find out that school C will not let weak students sit the exam as it spoils their percentage. We now think that A is the best school as the results for school C don’t represent the situation correctly.
Exam results • From George’s results we know his best subject is mathematics and his worst subject is Economics. • True or False?
Comment on features that are misleading. • Inappropriate graph. It does not show the data correctly. Data is discrete and yet this shows data as continuous. • Should have been a bar graph.
Comment on features that are misleading. • Scale on y-axis is not uniform. • Suppression of ‘0’. I.e. the graph does not start at zero. • Non-uniform scale on the x-axis.
Comment on the features that are misleading. • No units on the vertical axis. • As the height increases so does the width (and thickness) and visual impact of area (and volume) gives a distorted impression. • Not clear where carrots should be read from.
Misleading data The Minister of Consumer Affairs says that suits are really cheaper in 1982 than 1971. Explain his reasoning.
