1 How are the mean and median affected by skewing 2 When is

1. How are the mean and median affected by skewing.

2. When is the mean and the standard deviation appropriate to describe a data set?

3. What characteristic of a boxplot would indicate skewing?

4. In a boxplot, how is the width of the box related to spread?

5. How and why are split stems used in a stemplot?

Solution

1.

Mean is affected by skewness of distribution while median remains unaffected. If the distribution is skewed to left mean will be less than median while if distribution is skewed to right then mean is greater than median. And if the distribution is symmetric, then mean and median are apprximately equal.

2.

When the distribution is approximately symmetric and have no outlier then mean and standard deviation are appropriate.

If distribution has outlier and it is not symnetric, then median and interquartile range should be used.