1. Tilen threw a game die. In the table, he presented the number of throws for each number of points.

| number of points | 1 | 2 | 3 | 4 | 5 | 6 |
| :--- | :---: | :---: | :---: | :---: | :---: | :---: |
| number of throws | $3(x-2)$ | $2 x$ | $2(x-1)$ | $x+2$ | $2 x+1$ | $x$ |

a) How many times did he roll each number of points if the number of sixes represents exactly $10 \%$ of all throws?

b) Calculate the average number of points rolled.

c) Draw a frequency pie chart.

(6 points)
1. a) We calculate the total number of throws

$3(x-2)+2 x+2(x-1)+x+2+2 x+1+x=11 x-5$. We write the equation

$10 \%(11 x-5)$ or $11 x-5=10 x$. We solve the linear equation and get the solution, i.e., the number of sixes $x=5$. With the calculated $x$, we can then determine the number of throws for each number: one has landed 9 times, two 10 times, three 8 times, four 7 times, and five 11 times.

b) We calculate the average number of dots using the formula for the arithmetic mean $\frac{1 \cdot 9+2 \cdot 10+3 \cdot 8+4 \cdot 7+5 \cdot 11+6 \cdot 5}{50}=3.32$.

c) We calculate the size of the central angle for each number of dots: one: $\frac{9}{50} \cdot 360^{\circ}=$ $64.8^{\circ}$, two: $\frac{10}{50} \cdot 360^{\circ}=72^{\circ}$, three: $\frac{8}{50} \cdot 360^{\circ}=57.6^{\circ}$, four: $\frac{7}{50} \cdot 360^{\circ}=50.4^{\circ}$, five: $\frac{11}{50} \cdot 360^{\circ}=79.2^{\circ}$, and six: $\frac{5}{50} \cdot 360^{\circ}=36^{\circ}$.
Writing the equation $10 \%(11 x-5)=x$ ..... $1^{*}$ point
Solution of the equation $x=5$. . . ..... 1 point
Writing the answer ..... 1 point
Calculated average number of dots 3.32 ..... 1 point
Calculated central angles ..... $1^{*}$ point
Drawing the frequency pie chart ..... 1 point