Answer :
Let's analyze each of the statements about skewness and measures of center (mode, median, mean) to determine their validity:
1. Left Skewed is also known as under-skewed.
- Explanation: When a distribution is left-skewed, it means that the left tail (where the lower values are) is longer than the right tail. It's commonly known as negatively skewed, not under-skewed. Therefore, this statement is false.
2. The mode tends to be farther out on a tail.
- Explanation: The mode is the value that appears most frequently in a data set. In a skewed distribution, the mode is typically near the peak (the highest point) of the distribution, not in the tail. Therefore, this statement is false.
3. The mean is always to the right of the median.
- Explanation: In a left-skewed distribution, the mean is less than the median. In a right-skewed distribution, the mean is greater than the median. The mean is not always to the right of the median; it depends on the direction of skewness. Therefore, this statement is false.
4. The median is farther from the high point than the mean.
- Explanation: The median is the middle value of a data set, which divides the distribution into two equal parts. Depending on the skewness of the distribution, the median can be closer to the high point (the peak) than the mean. Therefore, this statement is false.
Given that all the provided statements are false, the correct answer is:
None of these are true.
This corresponds to the last option: None of these are true.
1. Left Skewed is also known as under-skewed.
- Explanation: When a distribution is left-skewed, it means that the left tail (where the lower values are) is longer than the right tail. It's commonly known as negatively skewed, not under-skewed. Therefore, this statement is false.
2. The mode tends to be farther out on a tail.
- Explanation: The mode is the value that appears most frequently in a data set. In a skewed distribution, the mode is typically near the peak (the highest point) of the distribution, not in the tail. Therefore, this statement is false.
3. The mean is always to the right of the median.
- Explanation: In a left-skewed distribution, the mean is less than the median. In a right-skewed distribution, the mean is greater than the median. The mean is not always to the right of the median; it depends on the direction of skewness. Therefore, this statement is false.
4. The median is farther from the high point than the mean.
- Explanation: The median is the middle value of a data set, which divides the distribution into two equal parts. Depending on the skewness of the distribution, the median can be closer to the high point (the peak) than the mean. Therefore, this statement is false.
Given that all the provided statements are false, the correct answer is:
None of these are true.
This corresponds to the last option: None of these are true.
