The survey is misleading because the sample sizes are

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The survey is misleading because the sample sizes are different. Arguing that there are now ten times more diseased fish is incorrect because it ignores the sample sizes. If students have calculated proportions or percentages, they will get a better sense of the data than if they rely on numbers: Two years ago: This year: Using this to argue that the number of diseased fish has doubled is still a misleading use of statistics: finding slightly more or fewer diseased fish in either survey (due to weather, the way the fish were caught, or just ‘the luck of the draw’) would make a big difference to the percentages. The judge could argue that the survey is poor evidence because the sample sizes are too small to detect a difference in such a small percentage of diseased fish. Or the judge might argue that there are not enough survey sites to show whether being downstream of the factory makes a difference. The reduced flow rate of the river might have affected the health of the fish regardless of the pollution. Why did the second survey look at so many more fish than the first: were the fish harder to find the first time? The number of invertebrates has not changed. There has been hardly any change in the mean number of invertebrates. Two years ago the mean across four sites was 21, and now it is 19. However, two years ago the range was 4. Now the range is 20. This is a big increase. The sites most likely to have been affected by the pollution are A and B, downstream from the factory. Two years ago the mean number of invertebrates at these sites was 21, now it is 12. This is quite a large decrease. In contrast, the mean at sites C and D has increased. Arguing that the mean number of invertebrates has hardly changed is a misuse of statistics: taking the mean of all four sites (including two which would not have been affected by pollution from the factory) hides the possibly significant reduction at the polluted sites. 6 300 × 100 = 2% 64 1600 × 100 = 4%
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Teacher guide Interpreting Data: Muddying the Waters T-11 The number of birds has increased. Using a line graph to represent this data is inappropriate because it gives the impression that the birds were continually monitored. A bar chart with two bars would be more appropriate. The scale on the line graph is misleading because it gives the impression that there has been a dramatic increase in the number of birds. The data show that there has only been an increase of 6 birds (about 7%). This is insignificant, especially without more details of how the birds were counted or at what time of year. Arguing that the chart shows that the number of birds has increased dramatically in the last two years is a misleading use of statistics. Assessment task: Unhappy Campers Question 1: Interpreting the scatter chart: There are fourteen data points on the scatter chart; the survey took place over a two-week period.
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