The lengths of boats in a harbor, in feet, are listed below.
17, 16, 56, 50, 14, 30, 12, 33, 82, 16, 10, 52, 25, 25, 19, 75, 24, 12, 30, 12, 20, 38, 26, 36, 33, 24, 18, 26, 40, 40
(a) Make a frequency table for the data set. Use 5-14 as the first class interval.
(b) Use the table to draw a histogram.
(c) Describe the type of distribution. Identify the relationship of the mean and the median.
For (a) I distributed the numbers following the fashion of 5-14. In other words like this:
5-14
15-23
24-32
33-41
42-50
51-59
60-69
70-79
I also made the histogram for (b).
I don't understand what (c) is asking though. Is it asking me to identify what shape the histogram is making? And what does it mean by identify the relationship between the mean and the median?
I appreciate any help!
Thank you!
I messed up a little bit in (a). It should actually be
5-14
15-23
24-32
33-41
42-50
51-59
60-68
70-78
79-87
For part (c) of the question, you are asked to describe the type of distribution and identify the relationship between the mean and the median.
To describe the type of distribution, you can observe the shape of the histogram you created in part (b). Look for any distinct patterns, such as symmetric, skewed, or uniform.
- A symmetric distribution means that the data is evenly spread out on both sides of the central value. It forms a bell-shaped curve.
- A skewed distribution means that the data tends to cluster more on one side than the other. If the tail of the histogram is longer on the left side, it is left-skewed, and if it is longer on the right side, it is right-skewed.
- A uniform distribution means that the data is evenly distributed across the range of values, forming a flat histogram.
Once you have described the type of distribution, you need to identify the relationship between the mean and the median.
- If the mean and median are approximately equal, it indicates a symmetric distribution or a uniform distribution.
- If the mean is greater than the median, it suggests a right-skewed distribution.
- If the mean is less than the median, it suggests a left-skewed distribution.
By determining the type of distribution and the relationship between the mean and the median, you can gain insights into the overall characteristics and tendencies of the data set.