AC 2.7: Mean, median, mode and weighted mean

Seven pupils score 4, 5, 5, 6, 7, 8 and 20 in a quiz. A teacher asks for the typical score.

She could say 5, or 6, or 8. Each answer is right for its own kind of average. Choosing the right one is part of the job.

The mean uses every value, so it is pulled by the 20. The median ignores how far out the 20 is. The mode is the most common, and is the only one that works for text such as the most popular colour.

For skewed data or outliers, the median is usually the fairest typical value.

scores = [4, 5, 5, 6, 7, 8, 20]
total = 0
for s in scores:
    total = total + s
print("mean", total / len(scores))

ordered = sorted(scores)
print("median", ordered[len(ordered) // 2])

best = 0
best_value = 0
for s in scores:
    count = scores.count(s)
    if count > best:
        best = count
        best_value = s
print("mode", best_value)

# Change the 20 to 8. Which average moves most?

Sometimes values do not count equally. A course mark may count the exam twice as much as each of two projects.

Multiply each mark by its weight, add the answers, and divide by the total of the weights. It is a mean where the exam counts double.