Question

Describe the shape of the data summarized in the histograms.​

Answer 1

Answers:

• 5) Roughly symmetrical
• 6) Skewed to the right (aka "right skewed" or "positively skewed")

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Explanation:

• 5) We don't have perfectly symmetrical data, as that would require the left half to be a perfect mirror copy of the right half. However, we have some semblance of symmetry going on. In the middle is 5 which is where the highest bar is, where the mode is located. The mean and median are likely to be around here as well. Then on either side of this highest peak are bars of shorter heights. The heights decrease as we move away from the center in either direction. We can draw an estimated or approximated bell curve (aka normal distribution curve or gaussian curve) to get a fairly good sense of how the data is roughly symmetric. The right-hand portion of this graph is shorter compared to the left side, but I don't think that's enough info to say if we have skewed data or not; so I would stick with "roughly symmetric" here.
• 6) Unlike problem 5, we don't have symmetric data. Instead, we have data that is skewed to the right. The main cluster is grouped or centered on the left side, while we have some outliers to the right side. Draw a curve over each peak of the bars and you'll see that the right tail is pulled longer than the left tail is. We consider this a positively skewed distribution because there are outliers in the positive x direction compared to the main cluster. In contrast, a negatively skewed distribution would have outliers smaller than the main cluster. The mean is larger than the median for a right-skewed distribution. This is due to the mean being pulled on by the outlier, while the median is robust and isn't affected by outliers no matter how distant they are.