Standard error of average customer spend

Question

A retailer surveys n = 400 customers and records how much each spent. The sample standard deviation of spending is s = \80. What is the standard error of the average customer spend?

Accepted Answer

Individual customers spend all over the map (spread about \80), but the average of 400 customers is a stable estimate of typical spending. The standard error of the mean measures how tightly that average is determined. Divide the person-to-person spread by the square root of the number surveyed: 	ext{SE} = \frac{s}{\sqrt{n}} = \frac{80}{\sqrt{400}} = \frac{80}{20} = \4. So even though people vary by roughly \80, the average spend is pinned down to within about \4, because \sqrt{400} = 20 shrinks the noise twentyfold. Takeaway. Standard error of the mean = s/\sqrt{n}: a survey of 400 makes th…

Standard error of average customer spend

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