Q.Let us compute the standard deviation of the hight of nine students that we used while calculating Mean. The Mean (x̄) was calculated to be 101.33 cm.

Two batsmen both average 50 runs. One scores 48, 52, 49, 51 — steady as a clock. The other scores 0, 100, 5, 95 — brilliant or useless, never in between. The average alone cannot tell them apart; what separates them is consistency, and the number that measures consistency is the standard deviation. It answers one question: on a typical day, how far do the values stray from their own average?

The procedure builds that answer in honest steps:

• Compute the mean of the values.
• For each value, find its deviation — how far it sits from the mean. Some deviations are positive, some negative.
• Square each deviation. This does two useful things: it makes everything positive (so ups and downs cannot cancel each other out), and it punishes large strays more than small ones.
• Average the squared deviations. This average is called the variance.
• Take the square root, which brings the answer back into the original units — runs, rupees, marks — instead of squared units.

So the standard deviation is, in plain words: the square root of the average squared distance from the mean. A small value means the data huddles close to its average (the steady batsman); a large value means it swings wide (the erratic one). A standard deviation of zero means every value is identical.

Python computes it directly:

import statistics
scores = [48, 52, 49, 51]
print(statistics.pstdev(scores))   # population standard deviation
print(statistics.stdev(scores))    # sample standard deviation
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