Question
If a data set is skewed, and most of the data are at the lower end of the data, which is a better measure of center? Explain.
The range; it would be smaller in a skewed data set.
The mode; it would have to be at the lower end of the data.
The mean; it is not affected by high or low data in a data set.
The median; it is less sensitive to outliers in a data set.
The range; it would be smaller in a skewed data set.
The mode; it would have to be at the lower end of the data.
The mean; it is not affected by high or low data in a data set.
The median; it is less sensitive to outliers in a data set.
Answers
Answered by
GPT-4o mini
In a skewed data set where most of the data are at the lower end, the better measure of center is:
**The median; it is less sensitive to outliers in a data set.**
### Explanation:
- **Skewness** implies that the data distribution is not symmetric, which often means there are outliers or extreme values that can distort measures of central tendency.
- **Mean** is the average and is sensitive to extreme values. In a right-skewed distribution (with a long tail to the right), the mean will be pulled in the direction of the tail, and in a left-skewed distribution (with a long tail to the left), it can be pulled down by those lower values.
- **Median** represents the middle value when the data set is ordered. It effectively divides the data into two equal halves and is less influenced by outliers or extreme values, making it a more robust measure of central tendency in skewed distributions.
- **Mode** is the most frequently occurring value but does not necessarily reflect the center of the data effectively, especially in skewed distributions.
- **Range** measures the spread of the data, not the center, so it wouldn't be an appropriate measure of central tendency.
Therefore, in a skewed data set with most data at the lower end, the median is the most appropriate measure of center.
**The median; it is less sensitive to outliers in a data set.**
### Explanation:
- **Skewness** implies that the data distribution is not symmetric, which often means there are outliers or extreme values that can distort measures of central tendency.
- **Mean** is the average and is sensitive to extreme values. In a right-skewed distribution (with a long tail to the right), the mean will be pulled in the direction of the tail, and in a left-skewed distribution (with a long tail to the left), it can be pulled down by those lower values.
- **Median** represents the middle value when the data set is ordered. It effectively divides the data into two equal halves and is less influenced by outliers or extreme values, making it a more robust measure of central tendency in skewed distributions.
- **Mode** is the most frequently occurring value but does not necessarily reflect the center of the data effectively, especially in skewed distributions.
- **Range** measures the spread of the data, not the center, so it wouldn't be an appropriate measure of central tendency.
Therefore, in a skewed data set with most data at the lower end, the median is the most appropriate measure of center.