Question

In the blank next to the distribution shape, type YES if is most often appropriate to use the mean, or NO if it is not.

Answer 1

Answers:

1. Yes
2. No
3. No
4. Yes
5. Yes

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Explanations:

1. A bell shaped curve is symmetric, meaning one half is a mirror copy of the other half. The mean, median and mode are both at the same value: at the center (which is where the peak is located).
2. A bimodal curve is one where it has two peaks. This is because it has 2 modes. Both peaks are the same height. If one height was taller, then you'd only have 1 mode. The mean wouldn't be as useful because we'd lose information about the two different modes. The mean would be somewhere in between the two peaks, where not much data points reside.
3. A skewed distribution is one where the tail is pulled from the main group/cluster. This pulls on the mean to be distorted from the center. If the tail is pulled to the right (right-skewed or positively skewed) then the mean is larger than it should be. If the tail is pulled to the left (left-skewed or negatively skewed) then the mean is smaller than it should be. It's better to use the median in this case. Example: home prices where large mansions are large outliers to make the mean larger than it should be, so the median home price is used instead.
4. As discussed in part 1 above, the mean is useful here. A bell shaped curve is one type of symmetric curve, but there are infinitely many other kinds of symmetric curves possible. All that matters is that one side is reflected over the vertical center line to get the other half.
5. A uniform distribution is symmetric. If the left and right endpoints are p and q, then the mean (p+q)/2 is the center and it is useful.