Answer :
Final answer:
The mean length of the boats is 27.77 feet, the median length is 39.5 feet, there is no mode, and the range is 36.5 feet.
Explanation:
To analyze the lengths of the boats, we can use various statistical measures. Let's start by finding the mean, median, mode, and range of the given data:
- Mean: To find the mean, we add up all the lengths and divide by the total number of lengths. In this case, the sum of the lengths is 32 + 18.5 + 46.5 + 29.5 + 32 + 15 + 25.5 + 46 + 27.5 + 38 + 43.5 + 34 + 35.5 + 11 + 44.5 + 43.5 + 14 + 33.5 + 39.5 + 24.5 + 47.5 + 45.5 + 45 + 38 + 20 = 888.5. There are 32 lengths, so the mean is 888.5 / 32 = 27.77 feet.
- Median: To find the median, we arrange the lengths in ascending order: 11, 14, 15, 18.5, 20, 24.5, 25.5, 27.5, 29.5, 32, 33.5, 34, 35.5, 38, 38, 39.5, 43.5, 43.5, 44.5, 45, 45.5, 46, 46.5, 47.5. There are 32 lengths, so the middle value is the 16th length, which is 39.5 feet.
- Mode: The mode is the value that appears most frequently. In this case, there is no value that appears more than once, so there is no mode.
- Range: The range is the difference between the largest and smallest lengths. The largest length is 47.5 feet and the smallest length is 11 feet, so the range is 47.5 - 11 = 36.5 feet.
Therefore, the mean length of the boats is 27.77 feet, the median length is 39.5 feet, there is no mode, and the range is 36.5 feet.
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