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The question you have involves summarizing data points from Super Bowl scores. You are asked to:

1. Find the **median**.
2. Find the **lower and upper quartiles** (Q1 and Q3).
3. Make a histogram and describe the distribution.

### Let's go step by step:

#### a) Find the median:
- The data set consists of 50 values:  
`45, 47, 23, 30, 29, 27, 31, 22, 38, 46, 37, 66, 50, 37, 47, 44, 47, 54, 56, 59, 52, 36, 65, 39, 61, 69, 63, 75, 44, 56, 55, 53, 39, 41, 37, 69, 61, 45, 31, 50, 48, 56, 65, 52, 62, 74, 16, 51`.

   To find the **median**, the values need to be ordered from smallest to largest. The median will be the middle value(s), i.e., the 25th and 26th values (since there are 50 data points).

#### b) Find the quartiles:
- **Lower quartile (Q1)**: This is the median of the lower half of the data.
- **Upper quartile (Q3)**: This is the median of the upper half of the data.

#### c) Histogram and distribution description:
- After calculating the quartiles and median, you can choose the correct histogram based on the spread and concentration of the data.

Let me start by calculating the median and quartiles for you. I'll also give some details on how to describe the distribution. I'll calculate these values now.Here are the results for the Super Bowl scores:

- **Median**: 47.5 points
- **Lower quartile (Q1)**: 37.75 points
- **Upper quartile (Q3)**: 56.75 points

Now for **part c** (histogram and distribution description), you need to observe the shape of the distribution. Generally, you should check for:
- **Skewness**: Whether the data is symmetrical or skewed.
- **Spread**: Look at the range (minimum and maximum values) to determine how spread out the data is.
- **Centering**: This is around the median value.
  
If you'd like, I can help with more specific guidance based on the histogram options.

Do you have any questions about these calculations? Would you like more help with the histogram?

Here are five related questions to deepen your understanding:
1. What does the interquartile range (IQR) tell you about data spread?
2. How does skewness affect the mean and median?
3. What are outliers, and how would you identify them in this dataset?
4. How could you use a boxplot to represent this data?
5. How can the quartiles help identify the central tendency of a dataset?

**Tip**: Quartiles are particularly useful for identifying outliers, as values outside 1.5 times the interquartile range (IQR) are considered potential outliers.

How many points do football teams score in the Super Bowl? The total numbers of points scored by both teams in 50 of the first 54 Super Bowl games are as shown. Complete parts a through c.

Analyze the total points scored in 50 Super Bowl games. Learn how to calculate the median, lower quartile (Q1), and upper quartile (Q3), and make a histogram to describe the data distribution. This problem covers key statistical concepts suitable for Grades 9-12.

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