Last time you learned how the mean helps summarize data. But here's a crucial question: how confident should you be in that average?
When your coffee shop averages $817 daily, does that mean every future day will be exactly $817? Of course not!
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What might cause daily sales to vary?
Here's the key insight: your data is just a sample of all possible days. You've seen some days, but not all future days.
Think of it like tasting soup - you taste one spoonful to judge the whole pot. But what if that spoonful wasn't perfectly representative?
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How confident can you be about the whole pot?
This is where statistical uncertainty becomes crucial for business decisions. Your $817 average might really represent anywhere from $780 to $854 in true daily performance.
This range matters when making decisions about staffing, inventory, or expansion plans.
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Why would this uncertainty range be important for planning?
We measure this uncertainty with something called a confidence interval. Instead of saying "average is $817," we say "we're 95% confident the true average is between $780-$854."
This gives stakeholders a realistic picture of what to expect.
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Which statement would you find more helpful for planning?
The size of your uncertainty depends on two key factors. First, how much your data varies - if daily sales range from $200 to $1,400, you'll have more uncertainty than if they range from $800 to $834.
Second, how much data you have - more days of data means more confidence.
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Which would give you more confidence: 7 days or 70 days of data?
