Problems from 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.

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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.

$I 1 = [0, 10]$

$I 2 = [11, 17]$

$I 3 = [18, 32]$

$I 4 = [33, 36]$

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:

$\begin{array}{rcl} h_{i} & = & \frac{f_{i}}{a_{i}} \\ h_{0} & = & \frac{3}{11} = 0. \overset{―}{27} \\ h_{1} & = & \frac{3}{7} = 0.43 \\ h_{2} & = & \frac{1}{14} = 0.07 \\ h_{3} & = & \frac{5}{4} = 1, 25 \end{array}$

Solution:

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

$I 1 = [0, 10]$

$I 2 = [11, 17]$

$I 3 = [18, 32]$

$I 4 = [33, 36]$

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