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6. The table shows the number of points scored by the seventh and eighth grade girls basketball teams in each of their games this season. Construct a double box plot to represent the data for each team. Then use the double box plot to compare the data.




Points Scored per Game






Seventh Grade Team
Eighth Grade Team



39
36
40
27
34
36
47
40


35
29
36
29
39
38
45
43


31
38
30
34
42
41
45
42

Apply\newline66. The table shows the number of points scored by the seventh and eighth grade girls basketball teams in each of their games this season. Construct a double box plot to represent the data for each team. Then use the double box plot to compare the data.\newline\begin{tabular}{|c|c|c|c|c|c|c|c|}\newline\hline \multicolumn{44}{|c|}{ Points Scored per Game } \\\newline\hline \multicolumn{33}{|c|}{ Seventh Grade Team } & \multicolumn{44}{|c|}{ Eighth Grade Team } \\\newline\hline 3939 & 3636 & 4040 & 2727 & 3434 & 3636 & 4747 & 4040 \\\newline\hline 3535 & 2929 & 3636 & 2929 & 3939 & 3838 & 4545 & 4343 \\\newline\hline 3131 & 3838 & 3030 & 3434 & 4242 & 4141 & 4545 & 4242 \\\newline\hline\newline\end{tabular}

Full solution

Q. Apply\newline66. The table shows the number of points scored by the seventh and eighth grade girls basketball teams in each of their games this season. Construct a double box plot to represent the data for each team. Then use the double box plot to compare the data.\newline\begin{tabular}{|c|c|c|c|c|c|c|c|}\newline\hline \multicolumn{44}{|c|}{ Points Scored per Game } \\\newline\hline \multicolumn{33}{|c|}{ Seventh Grade Team } & \multicolumn{44}{|c|}{ Eighth Grade Team } \\\newline\hline 3939 & 3636 & 4040 & 2727 & 3434 & 3636 & 4747 & 4040 \\\newline\hline 3535 & 2929 & 3636 & 2929 & 3939 & 3838 & 4545 & 4343 \\\newline\hline 3131 & 3838 & 3030 & 3434 & 4242 & 4141 & 4545 & 4242 \\\newline\hline\newline\end{tabular}
  1. Organize Data: First, we need to organize the data for each team in ascending order to prepare for constructing the box plots.\newlineSeventh Grade Team in ascending order: 31,34,35,36,39,40,42,4731, 34, 35, 36, 39, 40, 42, 47\newlineEighth Grade Team in ascending order: 27,29,29,34,36,38,40,41,42,43,45,4527, 29, 29, 34, 36, 38, 40, 41, 42, 43, 45, 45
  2. Find Medians: Next, we find the median (the middle value) for each team's data. If there is an even number of data points, the median will be the average of the two middle numbers.\newlineSeventh Grade Team median: (36+39)/2=37.5(36 + 39) / 2 = 37.5\newlineEighth Grade Team median: (38+40)/2=39(38 + 40) / 2 = 39
  3. Determine Quartiles: Now, we determine the lower quartile (Q1Q_1, the median of the lower half of the data) and the upper quartile (Q3Q_3, the median of the upper half of the data) for each team.\newlineSeventh Grade Team Q1Q_1: (34+35)/2=34.5(34 + 35) / 2 = 34.5\newlineSeventh Grade Team Q3Q_3: (40+42)/2=41(40 + 42) / 2 = 41\newlineEighth Grade Team Q1Q_1: (29+34)/2=31.5(29 + 34) / 2 = 31.5\newlineEighth Grade Team Q3Q_3: (42+43)/2=42.5(42 + 43) / 2 = 42.5
  4. Identify Extremes: Identify the minimum and maximum values for each team's data.\newlineSeventh Grade Team minimum: 3131, maximum: 4747\newlineEighth Grade Team minimum: 2727, maximum: 4545
  5. Construct Box Plot: With the five-number summary (minimum, Q1Q_1, median, Q3Q_3, maximum) for each team, we can now construct the double box plot.
  6. Compare Team Data: After constructing the double box plot, we can compare the data for each team. We look at the range, interquartile range (IQR), median, and any potential outliers to compare the performance of the two teams.

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