91Ó°ÊÓ

The formula used: Sample mean$=\frac{1}{n}×\underset{i=1}{\overset{20}{∑}}{x}_i$

We've been handed a$20-$person random sample.

Let $x_i$be the ${\mathrm{τ}}^{\text{th}}$observation on wedding cost of the sample, for all $i=1,2,…,20$

$∴$Total wedding cost $=\underset{i=1}{\overset{20}{∑}}{x}_i$

$=526538$[Sum of the sample observation]

$∴$Sample mean$=\frac{1}{n}×\underset{i=1}{\overset{20}{∑}}{x}_i,n=$sample size $=20$

$=\frac{1}{20}×526538$

$=26326.9$

$∴$Mean wedding cost for the given sample is $\$26326.9$

The sample mean can be used to estimate the (point) population mean wedding cost.

$∴$ The estimated value of the population mean $\left(\widehat{\mathrm{μ}}\right)$

$=\$26326.9$

No, it's doubtful that the sample mean $\stackrel{¯}{x}$ will be exactly the same as the population mean $\mathrm{μ}$ We're attempting to guess (estimate) the population mean value solely by drawing a sample, or a subset of the population. As a result, some sampling error is unavoidable.