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Mobile App Chapter 2: Q. 5 (page 137)
What the mean means The figure below is a density curve. Trace the curve onto your paper.
(a) Mark the approximate location of the median. Justify your choice of location.
(b) Mark the approximate location of the mean. Justify your choice of location.
Use the 68-95-99.7 rule to estimate the percent of observations from a Normal distribution that fall in an interval involving points one, two, or three standard deviations on either side of the mean.
Short Answer
a. The median will be significantly to the right of the peak since it will be greater as the most common values grow..
b. Because the median is not affected by extremely large values as effectively as the mean, the mean also lies to the right of the median.
Step by step solution
Part(a) Step 1: Concept Introduction
To get the mean of a data set, divide by the number of values in it. The median is the point where the highest and lowest values meet.
Part(a) Step 2: Explanation
Because the tail of large values causes the median to grow as the most common values grow, the median will lie slightly to the right of the peak:
Part(b) Step 1: Concept Introduction
To get the mean of a data set, divide by the number of values in it. The median is the point where the highest and lowest values meet.
Part(b) Step 2: Explanation
Because the tail of large values causes the mean to become larger as the most common values, the mean will lie to the right of the peak.
Because the mean is influenced more strongly by extremely big numbers than the median, it is also to the right of the median.
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