1764. Out of 2000 parts, 400 were selected, the distribution of which by size is given by the following table:

| Size of parts, mm | $7,95-8,00$ | $8,00-8,05$ | $8,05-8,10$ | $8,10-8,15$ | $8,15-8,20$ | $8,20-8,25$ |
| :---: | :---: | :---: | :---: | :---: | :---: | :---: |
| Number of parts | 12 | 28 | 132 | 150 | 62 | 16 |

Find the sampling error when determining the mean in cases of repeated and unrepeated sampling.
Solution. First, we find the sample variance $\sigma^{2}$ using the method indicated in $\S 5$ of Chapter XVI: $\sigma^{2}=0.00272$. For repeated sampling, $\mu=\frac{\sigma_{0}}{\sqrt{n}}=\frac{\sigma}{\sqrt{n-1}}=\sqrt{\frac{0.00272}{400-1}}=0.00261$. Since $\sqrt{\frac{0.00272}{400}}=0.002608$, for large $n$, $\mu$ can be practically found using the formula $\frac{\sigma}{\sqrt{n}}$.

For non-repeated sampling, $\mu \approx \frac{\sigma}{V \sqrt{n}} \sqrt{1-\frac{n}{N}}=$

$$
=0.00261 \sqrt{1-\frac{400}{2000}}=0.00234
$$