Propose a list of $$12$$ elements that represent the results of a casino roulette, including integers from $$0$$ to $$36$$. Then, propose a few possible intervals to do a histogram, so that every bar has the same height and has $$4$$ rectangles. Finally, group the results by tens (including zero as the first one) and calculate the heights of the rectangles of the histogram of absolute frequencies.
Development:
- Results: $$0$$, $$0$$, $$9$$, $$13$$, $$13$$, $$16$$, $$21$$, $$33$$, $$34$$, $$34$$, $$35$$, $$36$$.
- The intervals are designed so that each one has 3 elements.
$$I1= [0,10]$$
$$I2 = [11, 17]$$
$$I3 = [18, 32]$$
$$I4= [33,36]$$
- The following table shows the number of elements in every ten:
| $$[0,10]$$ | $$3$$ |
| [11, 17] | $$3$$ |
| $$[18, 32]$$ | $$1$$ |
| $$[33,36]$$ | $$5$$ |
The heights of every rectangle are calculated:
$$$\displaystyle \begin{array} {rcl} h_i&=&\frac{f_i}{a_i} \\\\ h_0&=&\frac{3}{11}=0.\overline{27} \\\\ h_1&=&\frac{3}{7}=0.43 \\\\ h_2&=&\frac{1}{14}=0.07 \\\\ h_3&=&\frac{5}{4}=1,25\end{array}$$$
Solution:
Results: $$0$$, $$0$$, $$9$$, $$13$$, $$13$$, $$16$$, $$21$$, $$33$$, $$34$$, $$34$$, $$35$$, $$36$$.
$$I1= [0,10]$$
$$I2 = [11, 17]$$
$$I3 = [18, 32]$$
$$I4= [33,36]$$
$$\displaystyle \begin{array} {rcl} h_i&=&\frac{f_i}{a_i} \\\\ h_0&=&\frac{3}{11}=0.\overline{27} \\\\ h_1&=&\frac{3}{7}=0.43 \\\\ h_2&=&\frac{1}{14}=0.07 \\\\ h_3&=&\frac{5}{4}=1,25\end{array}$$