Question
Number of hours in one week students on a girls’ high school field hockey team spent exercising:14, 14, 14, 14, 15, 15, 15, 16, 16, 16, 16, 16, 17, 17, 17, 18, 18, 18, 18, 18 Which measure of variability—IQR or MAD— best describes the spread of the dataset?
IQR; the data distribution is symmetrical
IQR; the data distribution is skewed
MAD; the data distribution is symmetrical
MAD; the data distribution is skewed
IQR; the data distribution is symmetrical
IQR; the data distribution is skewed
MAD; the data distribution is symmetrical
MAD; the data distribution is skewed
Answers
GPT-4o mini
To determine which measure of variability (IQR or MAD) best describes the spread of the dataset, we first need to assess the characteristics of the data distribution.
1. **Data Set**:
- The hours of exercise: 14, 14, 14, 14, 15, 15, 15, 16, 16, 16, 16, 16, 17, 17, 17, 18, 18, 18, 18, 18.
- The data is mostly centered around the values 14 to 18.
2. **Symmetry and Skewness**:
- The data appears to be fairly symmetrical, as there are almost equal numbers of values below and above the median (which is 16).
- There isn’t a significant skew to the left or right; therefore, the distribution can be classified as symmetrical.
3. **Comparison of IQR and MAD**:
- **IQR (Interquartile Range)** is used to measure the spread of the middle 50% of the data and is particularly useful for datasets that may have outliers or are skewed.
- **MAD (Mean Absolute Deviation)** is used to measure the average distance of each data point from the mean, and it is more sensitive to every individual data point, which may not provide a clear indication of spread when the distribution is symmetrical.
Given that the data distribution is symmetrical, the IQR is typically preferred in this situation since it better captures the spread of the central portion of the dataset without being influenced by any potential outliers.
Thus, the best choice is:
**IQR; the data distribution is symmetrical.**
1. **Data Set**:
- The hours of exercise: 14, 14, 14, 14, 15, 15, 15, 16, 16, 16, 16, 16, 17, 17, 17, 18, 18, 18, 18, 18.
- The data is mostly centered around the values 14 to 18.
2. **Symmetry and Skewness**:
- The data appears to be fairly symmetrical, as there are almost equal numbers of values below and above the median (which is 16).
- There isn’t a significant skew to the left or right; therefore, the distribution can be classified as symmetrical.
3. **Comparison of IQR and MAD**:
- **IQR (Interquartile Range)** is used to measure the spread of the middle 50% of the data and is particularly useful for datasets that may have outliers or are skewed.
- **MAD (Mean Absolute Deviation)** is used to measure the average distance of each data point from the mean, and it is more sensitive to every individual data point, which may not provide a clear indication of spread when the distribution is symmetrical.
Given that the data distribution is symmetrical, the IQR is typically preferred in this situation since it better captures the spread of the central portion of the dataset without being influenced by any potential outliers.
Thus, the best choice is:
**IQR; the data distribution is symmetrical.**