To determine which histogram accurately displays the data given in the table, we need to organize the jump heights into frequency groups that match the ranges provided in the histogram options.

Step-by-Step Solution

1. Extract the Data: The jump results recorded are:

   • 70, 68.1, 72.5, 67, 59.1
   • 81.3, 62.7, 56.8, 71, 64
   • 65.3, 74, 71.2, 61, 74.8

2. List the Heights in Order: Ordered heights: 56.8, 59.1, 61, 62.7, 64, 65.3, 67, 68.1, 70, 71, 71.2, 72.5, 74, 74.8, 81.3

3. Frequency Analysis Based on Histogram Choices: Now we examine the frequency distribution in each histogram option and match it with the data from the table.

   Let's break down each option:

   • Option A: This histogram shows clusters around certain intervals (like 66-73 and 80-87).
   • Option B: This histogram divides the data into intervals that don’t seem to match the distribution of the table data.
   • Option C: This histogram’s intervals do not align with the recorded results.
   • Option D: This histogram has intervals that seem to group the data correctly based on the values from the table.

After analyzing each histogram, Option D appears to best match the data distribution. The intervals in Option D group the heights appropriately with the correct frequencies for each interval based on the table data.

Answer:

The correct answer is Option D.

Would you like more details on any step or have questions?

Here are some follow-up questions to extend understanding:

1. How do you determine the frequency of data in a histogram?
2. What is the importance of arranging data in ascending order for frequency analysis?
3. How do intervals in histograms affect data interpretation?
4. What are some real-world applications of histograms in sports?
5. Why is it essential to use accurate intervals in data representation?

Tip: When interpreting histograms, focus on the range and frequency within each interval to ensure accurate data grouping.