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In this chapter, you will use the mean, median, mode and standard deviation of a set of data to identify whether the data is normally distributed or whether it is skewed. You will learn more about populations and selecting different kinds of samples in order to avoid bias. You will work with lines of best fit, and learn how to find a regression equation and a correlation coefficient. You will analyse these measures in order to draw conclusions and make predictions.
You are given a table of data below.
75 | 67 | 70 | 71 | 71 | 73 | 74 | 75 |
80 | 75 | 77 | 78 | 78 | 78 | 78 | 79 |
91 | 81 | 82 | 82 | 83 | 86 | 86 | 87 |
If large numbers of data are collected from a population, the graph will often have a bell shape. If the data was, say, examination results, a few learners usually get very high marks, a few very low marks and most get a mark in the middle range. We say a distribution is normal if
What happens if the test was very easy or very difficult? Then the distribution may not be symmetrical. If extremely high or extremely low scores are added to a distribution, then the mean tends to shift towards these scores and the curve becomes skewed.
If the test was very difficult, the mean score is shifted to the left. In this case, we say the distribution is positively skewed , or skewed right . If it was very easy, then many learners would get high scores, and the mean of the distribution would be shifted to the right. We say the distribution is negatively skewed , or skewed left .
Test Score | Frequency |
3 | 1 |
4 | 7 |
5 | 14 |
6 | 21 |
7 | 14 |
8 | 6 |
9 | 1 |
Total | 64 |
Mean | 6 |
Standard Deviation | 1,2 |
Speed (km.h ${}^{-1}$ ) | Number of cars (Frequency) |
50 | 19 |
60 | 28 |
70 | 23 |
80 | 56 |
90 | 20 |
100 | 16 |
110 | 8 |
120 | 5 |
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