Statistics

At a weather station in Las Vegas wind speeds were measured every day at $7$pm during one month. The results are specified in the following table. $$\begin{array}{|lcccccccc|}\hline \text{Day}& 1.& 2.& 3.& 4.& 5.& 6.& 7.& 8.\\ \text{Wind}(\mathrm{mps})& 3& 2& 1& 1& 2& 2& 1& 3\\ \\ \text{Day}& 9.& 10.& 11.& 12.& 13.& 14.& 15.& \\ \text{Wind}(\mathrm{mps})& 2& 1& 2& 2& 4& 2& 4& \\ \\ \text{Day}& 16.& 17.& 18.& 19.& 20.& 21.& 22.& 23.\\ \text{Wind}(\mathrm{mps})& 4& 2& 2& 3& 2& 12& 13& 6\\ \\ \text{Day}& 24.& 25.& 26.& 27.& 28.& 29.& 30.& \\ \text{Wind}(\mathrm{mps})& 5& 7& 2& 3& 8& 9& 12& \\ \hline\end{array}$$ Determine the median of the recorded wind speeds.

It is known that in the given time period one up to five pieces of the same product were sold in each of the 100 monitored shops. One piece was sold in $26$ shops, $2$ pieces in $64$ shops, $3$ pieces in $7$ shops, $4$ pieces in $2$ shops and $5$ pieces in one shop. How many pieces of the product were sold most frequently in the given shops? Choose the correct characteristic and its value.

Determine the number $x$ so that the geometric mean of the three numbers $(3;4.5;x)$ is $3$.

Determine the smallest integer value $x$ so that the arithmetic mean of the numbers $x$, $5$ and $6$ is greater than $20$.