Histogram

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.

  • 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:

$$\displaystyle \begin{array} {rcl} h_i&=&\frac{f_i}{a_i} \\\\ h_0&=&\frac{3}{11}=0.\overline{27} \\\\ h_1&=&\frac{3}{7}=0.43 \\\\ h_2&=&\frac{1}{14}=0.07 \\\\ h_3&=&\frac{5}{4}=1,25\end{array}$$

Results: $0$, $0$, $9$, $13$, $13$, $16$, $21$, $33$, $34$, $34$, $35$, $36$.

$$I1= [0,10]$$

$$I2 = [11, 17]$$

$$I3 = [18, 32]$$

$$I4= [33,36]$$

$$\displaystyle \begin{array} {rcl} h_i&=&\frac{f_i}{a_i} \\\\ h_0&=&\frac{3}{11}=0.\overline{27} \\\\ h_1&=&\frac{3}{7}=0.43 \\\\ h_2&=&\frac{1}{14}=0.07 \\\\ h_3&=&\frac{5}{4}=1,25\end{array}$$

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