To determine which histograms accurately represent the given data, we need to consider the distribution of the jump lengths provided in the table. Here is a step-by-step solution without performing actual calculations:
1. List the data points given:
- 81.2, 62.8, 70.6, 74.4, 56.7
- 72.8, 61.3, 64.9, 59.2, 68.2
- 77.5, 67.2, 76.7, 71.1, 61.9
2. Group the data into appropriate intervals or bins. The intervals could be something like this, for example:
- 55 to 59.9 inches
- 60 to 64.9 inches
- 65 to 69.9 inches
- 70 to 74.9 inches
- 75 to 79.9 inches
- 80 to 84.9 inches
3. Count the frequency of data points in each interval:
- 55 to 59.9 inches: 2 (56.7, 59.2)
- 60 to 64.9 inches: 5 (62.8, 61.3, 64.9, 61.9)
- 65 to 69.9 inches: 3 (68.2, 67.2)
- 70 to 74.9 inches: 4 (70.6, 74.4, 72.8, 71.1)
- 75 to 79.9 inches: 2 (77.5, 76.7)
- 80 to 84.9 inches: 1 (81.2)
4. Based on these frequencies, compare the histograms given in the problem to see which ones accurately reflect this distribution of data.
5. A correct histogram would have:
- A bar from 55 to 59.9 inches with a height representing a frequency of 2
- A bar from 60 to 64.9 inches with a height representing a frequency of 5
- A bar from 65 to 69.9 inches with a height representing a frequency of 3
- A bar from 70 to 74.9 inches with a height representing a frequency of 4
- A bar from 75 to 79.9 inches with a height representing a frequency of 2
- A bar from 80 to 84.9 inches with a height representing a frequency of 1
Now, visually inspect the given histograms and match them with the described frequencies and intervals to identify the correct ones.
