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?
(1 point)
Responses
IQR; the data distribution is skewed
IQR; the data distribution is skewed
MAD; the data distribution is skewed
MAD; the data distribution is skewed
IQR; the data distribution is symmetrical
IQR; the data distribution is symmetrical
MAD; the data distribution is symmetrical
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?
(1 point)
Responses
IQR; the data distribution is skewed
IQR; the data distribution is skewed
MAD; the data distribution is skewed
MAD; the data distribution is skewed
IQR; the data distribution is symmetrical
IQR; the data distribution is symmetrical
MAD; the data distribution is symmetrical
Answers
GPT-4o mini
To determine which measure of variability—Interquartile Range (IQR) or Mean Absolute Deviation (MAD)—best describes the spread of the dataset, we need to assess the distribution of the data.
1. **Data Distribution**: The dataset consists of the following values:
- 14, 14, 14, 14, 15, 15, 15, 16, 16, 16, 16, 16, 17, 17, 17, 18, 18, 18, 18, 18
These values are mostly clustered around the center (15 to 18), with a few repetitions at the lower extreme (14). There is no extreme skewness in the distribution, but it does have a slight tail towards the higher end (18 appears 5 times).
2. **Interquartile Range (IQR)**: This measure is used to describe the spread of the middle 50% of the data. It's more robust against outliers and skewness. Because the data is relatively close together and not extremely spread out, IQR would be a reasonable measure of variability.
3. **Mean Absolute Deviation (MAD)**: This measure considers the average distance of each data point from the mean. It can be influenced by the presence of outliers and is generally more sensitive to extreme values.
Given that the distribution shows a slight skewness towards the higher end but is not extremely skewed, the **IQR is more appropriate** for summarizing the spread of the dataset in this case.
**Correct Response: IQR; the data distribution is skewed.**
1. **Data Distribution**: The dataset consists of the following values:
- 14, 14, 14, 14, 15, 15, 15, 16, 16, 16, 16, 16, 17, 17, 17, 18, 18, 18, 18, 18
These values are mostly clustered around the center (15 to 18), with a few repetitions at the lower extreme (14). There is no extreme skewness in the distribution, but it does have a slight tail towards the higher end (18 appears 5 times).
2. **Interquartile Range (IQR)**: This measure is used to describe the spread of the middle 50% of the data. It's more robust against outliers and skewness. Because the data is relatively close together and not extremely spread out, IQR would be a reasonable measure of variability.
3. **Mean Absolute Deviation (MAD)**: This measure considers the average distance of each data point from the mean. It can be influenced by the presence of outliers and is generally more sensitive to extreme values.
Given that the distribution shows a slight skewness towards the higher end but is not extremely skewed, the **IQR is more appropriate** for summarizing the spread of the dataset in this case.
**Correct Response: IQR; the data distribution is skewed.**