If a distribution is skewed to the left, which of the following is true of the data set? Select two answers.
A.
The mean and the median are equal.
B.
The median is the best measure of center.
C.
The IQR is the best measure of variation.
D.
The mean is the best measure of center.
E.
The mean absolute deviation is the best measure of variation.
I would say D and A.
i would say d and a
The sentence "If a distribution is skewed to the left" means that the tail of the distribution is towards the left side.
Based on this information, the two correct answers would be:
A. The mean and the median are equal.
- In a left-skewed distribution, the mean will be less than the median, so this statement is not true.
B. The median is the best measure of center.
- Since the median is resistant to the effects of skewness, it is a better measure of center for skewed distributions. Thus, this statement is true.
Therefore, the correct answers are B. The median is the best measure of center, and D. The mean is the best measure of center.
To determine the correct answers, let's start by understanding what it means for a distribution to be skewed to the left.
A distribution is skewed to the left (negatively skewed) when the tail of the distribution extends towards the left side and the majority of the data points are located towards the right side.
Now, let's evaluate each statement to determine which ones are true for a left-skewed distribution:
A. The mean and the median are equal.
This statement is not necessarily true for a left-skewed distribution. In fact, in a left-skewed distribution, the mean is typically less than the median. Therefore, we can eliminate option A.
B. The median is the best measure of center.
This statement is true for a left-skewed distribution. In skewed distributions, the median is generally a better measure of center because it is less affected by extreme values than the mean. Therefore, we can select option B.
C. The IQR is the best measure of variation.
This statement is not related to skewness and is not necessarily true for a left-skewed distribution. The Interquartile Range (IQR) is a measure of spread, not variation. We cannot determine the best measure of variation based solely on skewness, so we can eliminate option C.
D. The mean is the best measure of center.
This statement is not true for a left-skewed distribution since the mean is influenced by extreme values. The median is generally a better measure of center for skewed distributions. Therefore, we can eliminate option D.
E. The mean absolute deviation is the best measure of variation.
This statement is not related to skewness and is not necessarily true for a left-skewed distribution. The mean absolute deviation (MAD) is a measure of spread, not variation. We cannot determine the best measure of variation based solely on skewness, so we can eliminate option E.
Based on the analysis above, the two true statements for a left-skewed distribution are:
B. The median is the best measure of center.
C. The IQR is the best measure of variation.