a. Organize costs as an ordered array. b. Construct the frequency

iohanetc 2021-09-24 Answered
a. Organize costs as an ordered array.
b. Construct the frequency distribution and percentage distribution for the given data.
c. Explain that the basketball game is concentrated around which class group.

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pivonie8
Answered 2021-09-25 Author has 5666 answers

a) Data about the total cost (in dollars) of the attending basketball game at each of the 30 National Basketball Association arenas is given.
The given data is already ordered in the ascending order. Thus, the costs, as an ordered array, are:
222.67,262.50,262.67,276.40,278.00,290.83,292.87,298.00,318.67,324.33,332.93,345.09,346.70,380.67,398.55,418.14,422.45,423.50,429.00,441.00,492.71,505.77,539.68,571.50,585.20,696.33,718.50,726.40,789.20,878.20.
b) The total cost ranges from about $222 to about $879. The number of classes can be taken between 5 and 10. So, consider the number of classes to be 7.
Then, the interval width is calculated as:
\(\displaystyle\text{Interval width}={\frac{{\text{Highest value-Lowest value}}}{{\text{number of classes}}}}\)
\(\displaystyle={\frac{{{879}-{222}}}{{{7}}}}\)
\(\displaystyle={93.9}\)
An amount that simplifies the reading and interpretation of the frequency distribution is 100. So, 100 is chosen as the interval width, which creates 7 classes from $200 to $900.
Thus, the table of the frequency and percentage distributions is:
\(\begin{array}{|c|c|} \hline Cost$&Frequency(f)&Percentage=\frac{f}{30} \times 10\%\\ \hline 200-\text{less than 300}&8&\frac{8}{30} \times 100\%=26.7\%\\ \hline 300-\text{less than 400}&7&\frac{7}{30} \times 100\%=23.3\%\\ \hline 400-\text{less than 500}&6&\frac{6}{30} \times 100\%=20\%\\ \hline 500-\text{less than 600}&4&\frac{4}{30} \times 100\%=13.3\%\\ \hline 600-\text{less than 700}&1&\frac{1}{30} \times 100\%=3.3\%\\ \hline 700-\text{less than 800}&3&\frac{3}{30} \times 100\%=10.3\%\\ \hline 800-\text{less than 900}&1&\frac{1}{30} \times 100\%=3.3\%\\ \hline Total&30&100\%\\ \hline \end{array}\)
c) The frequency and percentage distribution of the total costs to attend the National Basketball Association is obtained in part b.
About 70% of the costs of the basketball arenas range between $200 and $500. Among them, 27% are concentrated between $200 and $300. About 30% of the costs of the basketball arenas range between $500 and $900. Among them, 13% are concentrated between $500 and $600, and 10% are concentrated between $700 and $800.

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