Question
Compare and interpret the measures to select the data with the least variation.
DATA SET MEAN STANDARD DEVIATION
A 21 1.9
B 29 1.41
C 25 1.2
D 48 1.14
Dataset A has a standard deviation of 1.9 and a mean of 21. Dataset A has a standard deviation of 1.9 and a mean of 21. Dataset D has a standard deviation of 1.14 and a mean of 48. Dataset D has a standard deviation of 1.14 and a mean of 48. Dataset C has a standard deviation of 1.2 and a mean of 25. Dataset C has a standard deviation of 1.2 and a mean of 25. Dataset B has a standard deviation of 1.41 and a mean of 29.
DATA SET MEAN STANDARD DEVIATION
A 21 1.9
B 29 1.41
C 25 1.2
D 48 1.14
Dataset A has a standard deviation of 1.9 and a mean of 21. Dataset A has a standard deviation of 1.9 and a mean of 21. Dataset D has a standard deviation of 1.14 and a mean of 48. Dataset D has a standard deviation of 1.14 and a mean of 48. Dataset C has a standard deviation of 1.2 and a mean of 25. Dataset C has a standard deviation of 1.2 and a mean of 25. Dataset B has a standard deviation of 1.41 and a mean of 29.
Answers
GPT-4o mini
To compare the data sets based on variation, we will focus on the standard deviation values, which quantify the amount of variation or dispersion in the data. Lower standard deviation values indicate that the data points tend to be closer to the mean, leading to less variation in the data set.
Here are the standard deviations for each data set:
- Dataset A: Standard Deviation = 1.9
- Dataset B: Standard Deviation = 1.41
- Dataset C: Standard Deviation = 1.2
- Dataset D: Standard Deviation = 1.14
Now, let's rank the data sets based on their standard deviation, from the least variation to the most variation:
1. **Dataset D**: Standard Deviation = 1.14
2. **Dataset C**: Standard Deviation = 1.2
3. **Dataset B**: Standard Deviation = 1.41
4. **Dataset A**: Standard Deviation = 1.9
### Interpretation:
- **Dataset D** has the least variation with a standard deviation of **1.14**. This indicates that the values in Dataset D are more closely clustered around the mean (48) compared to the other data sets.
- Following that, **Dataset C** has a standard deviation of **1.2**, which suggests slightly more variation than Dataset D but less than Datasets B and A.
- **Dataset B**, with a standard deviation of **1.41**, shows greater variation than Datasets D and C but less than Dataset A.
- Finally, **Dataset A** has the highest standard deviation of **1.9**, indicating the greatest dispersion of values relative to its mean (21).
In conclusion, **Dataset D** is the best choice if we are looking for the data set with the least variation among the four options provided.
Here are the standard deviations for each data set:
- Dataset A: Standard Deviation = 1.9
- Dataset B: Standard Deviation = 1.41
- Dataset C: Standard Deviation = 1.2
- Dataset D: Standard Deviation = 1.14
Now, let's rank the data sets based on their standard deviation, from the least variation to the most variation:
1. **Dataset D**: Standard Deviation = 1.14
2. **Dataset C**: Standard Deviation = 1.2
3. **Dataset B**: Standard Deviation = 1.41
4. **Dataset A**: Standard Deviation = 1.9
### Interpretation:
- **Dataset D** has the least variation with a standard deviation of **1.14**. This indicates that the values in Dataset D are more closely clustered around the mean (48) compared to the other data sets.
- Following that, **Dataset C** has a standard deviation of **1.2**, which suggests slightly more variation than Dataset D but less than Datasets B and A.
- **Dataset B**, with a standard deviation of **1.41**, shows greater variation than Datasets D and C but less than Dataset A.
- Finally, **Dataset A** has the highest standard deviation of **1.9**, indicating the greatest dispersion of values relative to its mean (21).
In conclusion, **Dataset D** is the best choice if we are looking for the data set with the least variation among the four options provided.