Question
In: Statistics and Probability
1. A distribution that is skewed right has mean 150. What can you say about the...
1. A distribution that is skewed right has mean 150. What can you say about the value of its median?
2. A sample of 7 numbers has mean 142 and standard deviation s = 0. What can you say about the values of the numbers? Be precise!
Solutions
Expert Solution
1. Since the distribution is skewed right, it has longer tail on the right side. Thus, we possibilities of observing large values but not as often as observing small values. This has an effect of increasing the mean (pulling the mean towards right). The median is mostly insensitive to such occassionaly occuring large values (or outliers) and since, the smaller values have high frequency, it is expected that the median won't shift right as much as the mean does. Hence, typically we can expect the mean to be larger than the median. Hence in this case, the median is smaller than 150.
2.
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