- Ben is studying the Daily Total Rainfall, \(x \mathrm {~mm}\), in Leeming for 1987
He used all the data from the large data set and summarised the information in the following table.
| \(x\) | 0 | \(0.1 - 0.5\) | \(0.6 - 1.0\) | \(1.1 - 1.9\) | \(2.0 - 4.0\) | \(4.1 - 6.9\) | \(7.0 - 12.0\) | \(12.1 - 20.9\) | \(21.0 - 32.0\) | \(\operatorname { tr }\) |
| Frequency | 55 | 18 | 18 | 21 | 17 | 9 | 9 | 6 | 2 | 29 |
- Explain how the data will need to be cleaned before Ben can start to calculate statistics such as the mean and standard deviation.
Using all 184 of these values, Ben estimates \(\sum x = 390\) and \(\sum x ^ { 2 } = 4336\)
- Calculate estimates for
- the mean Daily Total Rainfall,
- the standard deviation of the Daily Total Rainfall.
Ben suggests using the statistic calculated in part (b)(i) to estimate the annual mean Daily Total Rainfall in Leeming for 1987
- Using your knowledge of the large data set,
- give a reason why these data would not be suitable,
- state, giving a reason, how you would expect the estimate in part (b)(i) to differ from the actual annual mean Daily Total Rainfall in Leeming for 1987