Answered

During the 2016-2017 season, the University of South Carolina Men's Basketball team made it to the final four. The Lady Gamecocks made it to the final four and won the National Championship. Below are the number of points each team scored during each of the games they played during the 2016-2017 season. Use the back-to-back stem and leaf plot to answer the questions.

\begin{tabular}{|c|c|c|c|}
\hline & Men's Team & & Women's Team \\
\hline & 743 & 5 & 59 \\
\hline 9877 & 64433210 & 6 & 0022345667 \\
\hline 9777 & 76300000 & 7 & 0112345699 \\
\hline & 886521 & 8 & 0123349 \\
\hline & \begin{tabular}{l}
8320
\end{tabular} & 9 & \begin{tabular}{l}
\begin{tabular}{ll}
0223358 \\
0 &
\end{tabular}
\end{tabular} \\
\hline Key: 3 I & [tex]$5=53$[/tex] points & & Key: [tex]$5 \mid 9=59$[/tex] Points \\
\hline
\end{tabular}

1. How many games did each team play?

The men played [tex]\(\boxed{40}\)[/tex] games and the women played [tex]\(\boxed{40}\)[/tex] games.

2. What is the mean points of each team?

The men scored an average of [tex]\(\boxed{53}\)[/tex] points and the women scored an average of [tex]\(\boxed{43}\)[/tex] points (round to the nearest point).

3. What is the range of the points of each team?

The men scored a range of [tex]\(\boxed{54}\)[/tex] points and the women scored a range of [tex]\(\boxed{38}\)[/tex] points.

4. What is the population standard deviation for each team?

The men had a standard deviation of [tex]\(\boxed{10.16}\)[/tex] points and the women had a standard deviation of [tex]\(\boxed{6.32}\)[/tex] points (round to nearest hundredth).

5. Based on the standard deviation, which team's points varied more?

The [tex]\(\boxed{women's}\)[/tex] team's points varied more based on the standard deviation.



Answer :

GinnyAnswer
Sure! Let's go through each of the questions step-by-step, using the data you provided and the summarized results from the calculations.

1. How many games did each team play?
- By tallying the number of points recorded for each team:
- Men played 17 games.
- Women played 13 games.

Therefore, the answer is:
```
The men played 17 games and the women played 13 games.
```

2. What is the mean number of points for each team?
- The mean or average is found by summing all the points scored and then dividing by the number of games.
- Men averaged 340 points.
- Women averaged 69 points.

Therefore, the answer is:
```
The men scored an average of 340 points and the women scored an average of 69 points.
```

3. What is the range of the points for each team?
- The range is calculated by subtracting the lowest score from the highest score:
- Men's range = Highest point - Lowest point = 987 - 20 = 967 points.
- Women's range = Highest point - Lowest point = 89 - 65 = 24 points.

Therefore, the answer is:
```
The men scored a range of 967 points and the women scored a range of 24 points.
```

4. What is the population standard deviation for each team?
- The standard deviation provides a measure of how much the points vary from the average:
- Men's standard deviation = 387.81 points.
- Women's standard deviation = 8.1 points.

Therefore, the answer is:
```
The men had a standard deviation of 387.81 points and the women had a standard deviation of 8.1 points.
```

5. Based on the standard deviation, which team's points varied more?
- To determine which team's points varied more, look at which standard deviation is higher:
- Men's standard deviation = 387.81 points.
- Women's standard deviation = 8.1 points.

Hence, the men's points varied more.

Therefore, the answer is:
```
Based on the standard deviation, the men's team's points varied more.
```

To summarize:
1. The men played 17 games and the women played 13 games.
2. The men scored an average of 340 points and the women scored an average of 69 points.
3. The men scored a range of 967 points and the women scored a range of 24 points.
4. The men had a standard deviation of 387.81 points and the women had a standard deviation of 8.1 points.
5. Based on the standard deviation, the men's team's points varied more.