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The question asks about the 77th percentile in a distribution of scores at a photography contest, where there are 1,000 entries and a score of 68 corresponds to the 77th percentile. To interpret this, let's first recall the concept of percentiles:

- The **77th percentile** means that 77% of the entries scored less than or equal to 68.
- The remaining 23% of the entries scored higher than 68.

Now, let's analyze the options given:

- **A**: "There were 770 entries with a score less than or equal to 68."  
  This is correct. Since the 77th percentile means that 77% of the scores are less than or equal to 68, 77% of 1,000 is 770.

- **B**: "There were at least 230 entries with a score of 77."  
  This is incorrect. The question is about the score of 68, not 77, and 230 refers to 23% of the distribution, which is unrelated to this description.

- **C**: "There were 23% of the entries with a score less than or equal to 68."  
  This is incorrect. It confuses the meaning of percentiles. The 77th percentile means that 77% of the scores are less than or equal to 68, not 23%.

- **D**: "There were 77% of the entries with a score equal to 68."  
  This is incorrect. The 77th percentile does not mean that exactly 77% of the entries have a score of 68; rather, 77% have scores less than or equal to 68.

- **E**: "There were at least 77% of the entries with a score greater than 68."  
  This is incorrect. The percentile refers to the percentage of scores **less than or equal to** 68, not greater than 68.

Thus, the correct answer is **A**: There were 770 entries with a score less than or equal to 68.

Would you like further details on this topic? Here are 5 related questions to consider:
1. What is the difference between a percentile and a percentage?
2. How do you calculate a percentile given a dataset?
3. What does the median correspond to in terms of percentiles?
4. How would you calculate the 90th percentile in a similar situation?
5. How do outliers affect the calculation of percentiles?

**Tip**: Percentiles are useful for understanding the relative standing of a value within a dataset, especially when comparing scores or measurements across different scales.

At a photography contest, entries are scored on a scale from 1 to 100. At a recent contest with 1,000 entries, a score of 68 was at the 77th percentile of the distribution of all the scores. Which of the following is the best description of the 77th percentile of the distribution?

Learn how to interpret the 77th percentile in a distribution of 1,000 scores. Understand what it means when a score of 68 is at the 77th percentile and explore the key concepts of percentiles and percentages. Suitable for high school students.

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