How do we calculate the range of values that fall within standard deviations?


#1

Question

In the context of this exercise, how do we calculate the range of values that fall within certain numbers of standard deviations?

Answer

To determine the range of values, we first need the value of a single standard deviation for a dataset. With this value, it is easy to then calculate the ranges of values.

# Given: 
# std_dev = standard deviation of the dataset
# mean = mean of the dataset

# 68% of the data falls between +/- 1 standard deviation
one_std_range = [mean - std_dev, mean + std_dev]

# 95% of the data falls between +/- 2 standard deviations
two_std_range = [mean - (2*std_dev), mean + (2*std_dev)]

# 99.7% of the data falls between +/- 3 standard deviations
three_std_range = [mean - (3*std_dev), mean + (3*std_dev)]