Probability & the Empirical Rule, Z-scores, and Percentiles

what does the normal curve tell us?

• how common different values of your data are

• can think of it as a probability distribution

what is the benefit of knowing the normal curve?

• we can calculate the probability that any particular value will fall into different distances from the mean

  • the peak of the curve is the most likely value

  • end of the curve is are the rarest

the empirical rule

• when u have normally distributed data, you can use the empirical rule to understand what proportion of your data’s values fall within any specified number of standard deviations from the mean

• in normsl distribution

  • 68% of your data points will be within +- 1 standard deviation of the mean

  • 95% will be +-2 standard deviations

  • 99.7% will be within +- 3 standard deviations

what are Z-scores? (aka standard scores)

• statistic that tell you how many standard deviations any data point is from the mean of your sample

  • useful for understanding the relative rarity of any values in your data

• first step in figuring out the relatice rarity (or percentile) of any value in your data set.

how are z-scores calculated?

• subtracting the mean from the value

• dividing it by the standard deviation

z-table

• we use this table to translate the z-score into the ‘percentile’, or relative rarit of a value

• the percentile is the proportion of values which are lower than the value you’re testing