Estimate population mean and variance from a frequency table

Enter diameters in L 1 and frequencies in L 2. The source’s 1-Var Stats screen uses List:L 1 and FreqList:L 2. Its results give $\bar x=13$, $\sum x=1040$, $\sum x^2=13590$, $n=80$, sample standard deviation $S_x\approx0.941316073$ and population-style standard deviation $\sigma_x\approx0.9354143467$. The visible extra summaries are minX=11 and Q 1=12. Use $S_x^2$, not $S_x$ or $\sigma_x^2$, for the unbiased variance estimate. The estimates are $13$ mm and $(0.941316073\ldots)^2\approx0.886$ mm².

$\sum x=11(3)+12(22)+13(31)+14(20)+15(4)=1040$ and $\sum x^2=11^2(3)+12^2(22)+13^2(31)+14^2(20)+15^2(4)=13590$. Thus $\bar x=1040/80=13$ and $s^2=\dfrac{1}{79}\left(13590-\dfrac{1040^2}{80}\right)=\dfrac{70}{79}\approx0.886$ mm², to 3 s.f. These estimates use the recorded, rounded diameters.