In a positively skewed distribution, the mean is always*1 pointA. Smaller than the medianB. Equal to the medianC. larger than the medianD. equal to the mode
Question
In a positively skewed distribution, the mean is always*
1 point
A. Smaller than the median
B. Equal to the median
C. larger than the median
D. equal to the mode
Solution
To answer the question regarding the characteristics of a positively skewed distribution, let's analyze the concepts involved:
-
Understanding Positively Skewed Distribution: In a positively skewed distribution (also known as right-skewed), the tail on the right side of the distribution is longer or fatter than the left side. This indicates that there are a larger number of lower values and a few higher values.
-
Relationship Between Mean, Median, and Mode:
- In a positively skewed distribution, the mean is typically greater than the median due to the influence of the few higher values pulling the mean upwards.
- The median, being the middle value, remains unaffected by the extreme values in the tail, thus it is usually less than the mean.
- The mode is usually the highest point in the distribution and tends to be less than both the mean and median in a positively skewed distribution.
Given these points, the correct answer to the question is:
Final Answer
C. larger than the median
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