Describing data

Before any model, describe your data.

Centre

• Mean: the sum divided by the count.
• Median: the middle value once sorted (the average of the two middle ones for an even count).
• Mode: the most common value.

Spread

• Range: largest − smallest.
• Variance and standard deviation: the typical squared distance from the mean, and its square root. For a sample, divide by n − 1 instead of n; it corrects a small underestimate.

import statistics as st

marks = [62, 70, 70, 75, 81, 88, 91]
print("mean", round(st.mean(marks), 2), " median", st.median(marks), " mode", st.mode(marks))
print("range", max(marks) - min(marks), " sample SD", round(st.stdev(marks), 2))

marks.append(10)
print("after one outlier: mean", round(st.mean(marks), 2), " median", st.median(marks))

Outliers

One salary of 1,000,000 among nine of about 30,000 drags the mean far up, while the median barely moves. That is why news reports quote the median income.

Python's statistics module computes all of these: mean, median, mode, stdev (n − 1) and pstdev (n).

Mark lesson complete