Question
Robin’s scores: 99, 108, 102, 107, 119
Mean = 107; MAD = 5.2
Evelyn’s scores: 125, 137, 138, 145, 145
Mean = 138; MAD = 5.6
Explain what the mean absolute deviation is in general. Explain what the MAD means in the context of Robin and Evelyn’s data.
Mean = 107; MAD = 5.2
Evelyn’s scores: 125, 137, 138, 145, 145
Mean = 138; MAD = 5.6
Explain what the mean absolute deviation is in general. Explain what the MAD means in the context of Robin and Evelyn’s data.
Answers
GPT-4o mini
The Mean Absolute Deviation (MAD) is a statistical measure that quantifies the average absolute difference between each data point in a dataset and the mean of that dataset. It provides a way of understanding the variability or dispersion of the data around the mean. The formula for calculating the MAD is as follows:
1. Compute the mean of the dataset.
2. For each data point, calculate the absolute deviation from the mean (i.e., take the absolute value of the difference between each data point and the mean).
3. Average these absolute deviations.
The resulting value is expressed in the same units as the original data and provides insight into how spread out the values are around the mean.
### Context of Robin and Evelyn’s Data
**Robin's MAD:**
- Robin's scores are: 99, 108, 102, 107, 119.
- The calculated MAD for Robin is 5.2.
This means that, on average, Robin's scores are 5.2 points away from her mean score of 107. A smaller MAD indicates that her scores are relatively close to the mean, indicating less variability in her performance. In this case, Robin's scores cluster fairly closely around 107.
**Evelyn's MAD:**
- Evelyn's scores are: 125, 137, 138, 145, 145.
- The calculated MAD for Evelyn is 5.6.
This means that, on average, Evelyn's scores are 5.6 points away from her mean score of 138. While her mean score is higher than Robin's, her MAD is slightly higher as well, suggesting that Evelyn’s scores, while also relatively close to her mean, have a bit more variability than Robin's scores.
### Summary
In both cases, the MAD provides a numerical summary of how consistent each person's scores are around their respective means. Robin has a lower MAD, indicating less variability in her scores, while Evelyn has a slightly higher MAD, suggesting her scores fluctuate a bit more despite a higher overall average. This comparison helps in understanding not just the central tendency of their performances but also the consistency of those performances.
1. Compute the mean of the dataset.
2. For each data point, calculate the absolute deviation from the mean (i.e., take the absolute value of the difference between each data point and the mean).
3. Average these absolute deviations.
The resulting value is expressed in the same units as the original data and provides insight into how spread out the values are around the mean.
### Context of Robin and Evelyn’s Data
**Robin's MAD:**
- Robin's scores are: 99, 108, 102, 107, 119.
- The calculated MAD for Robin is 5.2.
This means that, on average, Robin's scores are 5.2 points away from her mean score of 107. A smaller MAD indicates that her scores are relatively close to the mean, indicating less variability in her performance. In this case, Robin's scores cluster fairly closely around 107.
**Evelyn's MAD:**
- Evelyn's scores are: 125, 137, 138, 145, 145.
- The calculated MAD for Evelyn is 5.6.
This means that, on average, Evelyn's scores are 5.6 points away from her mean score of 138. While her mean score is higher than Robin's, her MAD is slightly higher as well, suggesting that Evelyn’s scores, while also relatively close to her mean, have a bit more variability than Robin's scores.
### Summary
In both cases, the MAD provides a numerical summary of how consistent each person's scores are around their respective means. Robin has a lower MAD, indicating less variability in her scores, while Evelyn has a slightly higher MAD, suggesting her scores fluctuate a bit more despite a higher overall average. This comparison helps in understanding not just the central tendency of their performances but also the consistency of those performances.