Question

Why is the median​ resistant, but the mean is​ not?
Choose the correct answer below.
A.
The median is​ resistant, while the mean is​ not, because when there are extreme values in the​ tail, the value of the median changes while the mean does not.
B.
The mean is not resistant because when data are​ skewed, there are extreme values in the​ tail, which tend to pull the mean in the direction of the tail. The median is resistant because the median of a variable is the value that lies in the middle of the data when arranged in ascending order and does not depend on the extreme values of the data.
C.
The mean is not resistant because when data are​ skewed, there are extreme values in the​ tail, which do not pull the mean in that direction.​ However, the median is pulled in the direction of the extreme​ values, making it resistant.
D.
The mean is not resistant because it is dependent upon the sample​ size, n. The larger n​ is, the smaller the mean becomes.​ However, the median is resistant because it is not dependent on the sample​ size, n.

Answer 1

Answer:the answer is a

Step-by-step explanation:

Answer 2

Using the concepts of the mean and the median, the correct option is given by:

B.

The mean is not resistant because when data are​ skewed, there are extreme values in the​ tail, which tend to pull the mean in the direction of the tail. The median is resistant because the median of a variable is the value that lies in the middle of the data when arranged in ascending order and does not depend on the extreme values of the data.

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• The mean of a data-set is given by the sum of all of the values in the data-set divided by the cardinality of the data-set, that is, the number of values it has.
• The median is the 50th percentile, that is, the measure that splits the data-set, when sorted ascendingly, in half, one-half having the lower 50% of the measures, and the other having the upper 50%.
• From this, we can conclude that since the mean involves all values, it can be affected by outliers, which are values on the tails, while the median is not.
• Thus, the correct option, which states the bullet point above, is option b.

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