However, in numerical computations with the second form, one needs to take care not to round any intermediate results in order to prevent serious errors. Find the centroid of the region bounded by the Find the centroid of the region bounded by the given curves. ![]() To sum these values to obtain a sampling distribution, you can use spreadsheet programs such as Microsoft Excel or Google Sheets that have various prepackaged statistical tools for uses like these. Then $\hat\mu = \bar X = \frac 1n\sum_^n X_i^2 - n\bar X^2,$ where the first equality is by definition and the second by algebra. You can find the value of x-bar for any sample quickly by referring to a page like the one in the Resources. Population with $\mu$ and standard deviation $\sigma.$Įstimating the population mean. Suppose you have a random sample $X_1, X_2, \dots,X_n$ of size $n$ from a normal M
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