Normal Distributions – How Understanding Them Helps Shops Order the Right Number of Clothes

The normal distribution appears everywhere in statistics — from exam results and human height to machine tolerances and weather data. But it’s not just for maths lessons. Businesses use normal distributions every day to make smart, data-driven decisions — including something as simple (and important) as deciding how many of each clothing size to stock.

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The Concept

A normal distribution is the classic bell-shaped curve where most values cluster around the mean, and fewer appear at the extremes.
For example, if the average chest size for men is 100 cm with a standard deviation of 8 cm, the distribution of sizes will look like this:

• Around 68% of people fall within one standard deviation (92–108 cm).

• Around 95% fall within two standard deviations (84–116 cm).

That means most customers will need sizes around the middle — not the smallest or largest options.

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The Real-World Application

Shops use this kind of data to avoid overstocking or understocking certain sizes.
If a retailer orders the same quantity of every size, they’ll run out of mediums while being left with piles of XS and XXL shirts.

By analysing customer data, they can order according to the normal curve:

• Fewer extreme sizes

• More of the average

• Enough variation to meet most demand without waste

Understanding the mean, standard deviation, and percentiles helps businesses match supply to real customer needs — saving money and reducing unsold inventory.

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Example

If data show:

Size	% of Customers	Recommended Stock per 100 Items
XS	5%	5
S	15%	15
M	40%	40
L	30%	30
XL	10%	10

Then a retailer ordering 100 shirts would stock more mediums and larges — exactly what the normal distribution predicts.

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Skills Highlight

• Interpreting and applying the normal distribution

• Understanding mean, standard deviation, and probability

• Linking mathematical models to real business data

• Seeing how statistics drive practical decision-making

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Why It Works in Teaching

When students see how a mathematical curve can shape real commercial decisions, statistics stops being abstract. The normal distribution becomes a story about prediction, planning, and efficient use of resources — connecting classroom maths to everyday economics.