Which is true of positively skewed distributions?
I. They are not symmetrical.
II. Their mean is larger than their median.
III. They are characterized by many small values and a few extreme values.
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A. B. C. D.Explanation
All are true of positively skewed distributions, so the answer is I, II, and III: None of the above is the correct choice.
Positively skewed distributions, also known as right-skewed distributions, are characterized by a long tail on the right side of the distribution. This means that the majority of the data points in the distribution are clustered towards the left side, and there are relatively fewer data points towards the right side.
Let's go through each statement and determine if it is true for positively skewed distributions:
I. They are not symmetrical. This statement is true. Positively skewed distributions are not symmetrical because the tail on the right side pulls the distribution towards that direction. The bulk of the data is concentrated towards the left, resulting in an asymmetrical shape.
II. Their mean is larger than their median. This statement is true. In positively skewed distributions, the tail on the right side contains relatively few extreme values that are much larger than the majority of the data points. This results in an elongated right tail that pulls the mean towards higher values. Since the median represents the central value that separates the lower and upper halves of the distribution, it is less affected by extreme values and is generally closer to the majority of the data. Therefore, the mean is larger than the median in positively skewed distributions.
III. They are characterized by many small values and a few extreme values. This statement is true. Positively skewed distributions are characterized by a cluster of smaller values towards the left side of the distribution and a few extremely large values towards the right side. The majority of the data points are concentrated in the lower range, while the tail on the right side extends to higher values. This pattern contributes to the positively skewed shape.
Based on the explanations above, both statements I and II are true for positively skewed distributions. Therefore, the correct answer is:
A. I and II