Question
Tina and her friends have all seen the latest vampire movies. They each gave the movie a rating out of five stars. This line plot shows the results
Because this data is the most appropriate measure of spread would be
A. Skewed.
B. Symmetric.
Mean
Median
Standard deviation
Inter Quartile range
Because this data is the most appropriate measure of spread would be
A. Skewed.
B. Symmetric.
Mean
Median
Standard deviation
Inter Quartile range
Answers
GPT-4o mini
To determine the most appropriate measure of spread for the ratings given in the line plot, we need to consider the shape and distribution of the data.
1. **Skewed vs. Symmetric**: If the ratings are distributed unevenly, either with a long tail on one side (skewed) or balanced (symmetric), this impacts which measures of spread are appropriate.
2. **Mean vs. Median**: The mean is affected by extreme values (outliers), while the median is more robust and is less influenced by outliers. If the data is skewed, the median would typically be a better measure of central tendency and thus, the interquartile range (IQR) would be a better measure of spread.
3. **Standard Deviation**: This is a measure of spread that assumes a symmetric distribution; it is sensitive to outliers.
4. **Interquartile Range (IQR)**: This measure focuses on the middle 50% of the data and is not affected by outliers. It is a good measure of spread for skewed distributions.
Given this analysis, if the data is skewed, the most appropriate measure of spread would be the **Interquartile Range (IQR)**. If the data is symmetric, then the **Standard Deviation** could also be considered, but if we have any reason to suspect skewness, IQR is preferred.
Without seeing the actual line plot, if you suspect that the ratings are not normally distributed, the **IQR** would be the best choice. If they seem balanced with no outliers, you could consider standard deviation.
Therefore, the final answer would depend on the underlying data distribution:
- If Skewed: Interquartile Range (IQR)
- If Symmetric: Standard Deviation
1. **Skewed vs. Symmetric**: If the ratings are distributed unevenly, either with a long tail on one side (skewed) or balanced (symmetric), this impacts which measures of spread are appropriate.
2. **Mean vs. Median**: The mean is affected by extreme values (outliers), while the median is more robust and is less influenced by outliers. If the data is skewed, the median would typically be a better measure of central tendency and thus, the interquartile range (IQR) would be a better measure of spread.
3. **Standard Deviation**: This is a measure of spread that assumes a symmetric distribution; it is sensitive to outliers.
4. **Interquartile Range (IQR)**: This measure focuses on the middle 50% of the data and is not affected by outliers. It is a good measure of spread for skewed distributions.
Given this analysis, if the data is skewed, the most appropriate measure of spread would be the **Interquartile Range (IQR)**. If the data is symmetric, then the **Standard Deviation** could also be considered, but if we have any reason to suspect skewness, IQR is preferred.
Without seeing the actual line plot, if you suspect that the ratings are not normally distributed, the **IQR** would be the best choice. If they seem balanced with no outliers, you could consider standard deviation.
Therefore, the final answer would depend on the underlying data distribution:
- If Skewed: Interquartile Range (IQR)
- If Symmetric: Standard Deviation