Question
Explain how the shape of a distribution determines the appropriate measure of center.(1 point) Responses Skewed data means that the mean is the best measure of center. Skewed data means that the mean is the best measure of center. The shape does not matter when determining the appropriate measure of center. The shape does not matter when determining the appropriate measure of center. Symmetrical data means that the mean is the best measure of center. Symmetrical data means that the mean is the best measure of center. More information is needed to determine how the data of distribution determines the appropriate measure of center.
Answers
GPT-4o mini
The correct response is: **Symmetrical data means that the mean is the best measure of center.**
Here's why:
1. **Symmetrical Distribution**: In a symmetrical distribution (like a normal distribution), the mean, median, and mode are all located at the center, making the mean a reliable measure of center.
2. **Skewed Distribution**: In a skewed distribution (whether left or right), the mean can be pulled in the direction of the skew, making it less representative of the data center. In such cases, the median, which is not affected by extreme values, is typically a better measure of center.
So, the shape of the distribution significantly influences which measure of center (mean, median, or mode) is most appropriate.
Here's why:
1. **Symmetrical Distribution**: In a symmetrical distribution (like a normal distribution), the mean, median, and mode are all located at the center, making the mean a reliable measure of center.
2. **Skewed Distribution**: In a skewed distribution (whether left or right), the mean can be pulled in the direction of the skew, making it less representative of the data center. In such cases, the median, which is not affected by extreme values, is typically a better measure of center.
So, the shape of the distribution significantly influences which measure of center (mean, median, or mode) is most appropriate.