Use the given sorted values, which are the numbers of points scored in the Super Bowl for a recent period of 24 years. Find the percentile corresponding to the given number of points.

36 37 37 39 39 41 43 44 44 47 50 53 54 55 56 56 57 59 61 61 65 69 69 75

𝑃𝑘=65

k=

To find the percentile corresponding to the given number of points, \(P_k = 65\), we need to determine the position of the number 65 in the sorted list and then calculate the percentile rank.

### Step-by-Step Solution

1. **List the sorted values**:
   \[
   36, 37, 37, 39, 39, 41, 43, 44, 44, 47, 50, 53, 54, 55, 56, 56, 57, 59, 61, 61, 65, 69, 69, 75
   \]

2. **Find the position of the given value, 65**:
   - In the sorted list, the number 65 is the 21st value.

3. **Calculate the percentile rank**:
   The formula to find the percentile rank of a value in a data set is:
   \[
   P = \frac{L}{N} \times 100
   \]
   where:
   - \(P\) is the percentile rank.
   - \(L\) is the number of values less than the given value.
   - \(N\) is the total number of values in the dataset.

   In this case:
   - \(L = 20\) (since there are 20 values less than 65).
   - \(N = 24\) (the total number of values).

   Substituting these values into the formula gives:
   \[
   P = \frac{20}{24} \times 100 = \frac{5}{6} \times 100 \approx 83.\overline{3}
   \]

### Conclusion

The percentile corresponding to the given number of points, 65, is approximately the **83rd percentile**.

Would you like more details or have any questions about this solution?

### Related Questions:

1. What is the percentile rank for a score of 39 in this dataset?
2. How many points are at the 50th percentile (the median) in this dataset?
3. What is the range of the dataset?
4. Calculate the interquartile range (IQR) of the dataset.
5. What is the z-score for the value 65 in this dataset?

**Tip:** Remember, the percentile tells us the percentage of data points that are below a certain value.

Learn how to find the percentile corresponding to a given number of points scored in the Super Bowl. Step-by-step solution with a detailed calculation using the percentile formula. Suitable for high school students studying statistics.

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