ENVX1002 Lecture Notes - Lecture 8: Root Mean Square, Estimation Theory, Standard Score

• School: University of Sydney
• Department: Environmental Statistics
• Course: ENVX1002
• Professor: Di Warren

Document Summary

We could calculate the average of the gaps. From the definition of the mean, the mean gap must be 0, as the mean is the balancing point of the gaps. Or from looking at the formula this is to be expected by some algebra. The rms measures the average of the data, regardless of the signs. The standard deviation measures the spread of the data. It calculates the rms of the gaps from the mean. Applying the population standard deviation formula to the sample, underestimates the true population standard deviation. Hence we need an adjusted formula for the sample standard deviation where we divide by (1 / n-1) rather than (1 / n) For many data sets, we find that roughly : percentage of data distance from mean. Iqr : range of the middle 50% of the data = q3 - q1. Where q1 is the 25% (1st) percentile and q3 is the 75% (3rd) percentile.