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NV 07 /0 6 / 21 1 of (^2) Version 1.
Comparing data sets: Anscombe’s Quartet
Set 1 Set 2 Set 3 Set 4 x y x y x y x y 10 8. 04 10 9.14 10 7.46 8 6. 8 6.95 8 8.14 8 6.77 8 5. 13 7.58 13 8.74 13 12.74 8 7. 9 8.81 9 8.77 9 7.11 8 8. 11 8.33 11 9.26 11 7.81 8 8. 14 9.96 14 8.1 14 8.84 8 7. 6 7.24 6 6.13 6 6.08 8 5. 4 4.26 4 3.1 4 5.39 19 12. 12 10.84 12 9.13 12 8.15 8 5. 7 4.82 7 7.26 7 6.42 8 7. 5 5.68 5 4.74 5 5.73 8 6.
- Compare these data sets by calculating appropriate descriptive statistics.
- What’s the same & what’s different?
- How would you describe the correlation of each data set?
- How else could you investigate these data sets?
NV 07 /0 6 / 21 2 of (^2) Version 1. Teacher’s notes: Desmos file of data sets: https://www.desmos.com/calculator/6tdarsx61s These data are Anscombe’s Quartet. All 4 data sets have the same descriptive statistics to 2dp:
- mean x value is 9 for each dataset
- mean y value is 7.50 for each dataset
- Assuming each data set is a population: the variance for x is 10.0 & the variance for y is 3.75 to 3sf
- If students assume these are sample: the variance for x is 11.0 and the variance for y is 4.13 to 3sf
- The correlation between x and y is 0.816 for each dataset
- A linear regression (line of best fit) for each dataset follows the equation y = 0.5x + 3 Without plotting these data sets as scatter graphs, students may conclude that the PMCC value of 0. implies strong positive linear correlation and that the data sets are indistinguishable from each other. These are a great way to reinforce the importance of looking at data before drawing conclusions from descriptive statistics.
