To determine which measure of variability is the best to use when comparing the data for two brands of batteries, we need to analyze several aspects of the distribution of the data:
1. Central Tendency (Mean and Median):
- The mean and median provide insights into where the center of the data lies.
2. Variability (Standard Deviation and Interquartile Range):
- The standard deviation tells us about the dispersion of data around the mean.
- The interquartile range (IQR) measures the middle 50% of the data, which can give us insights into the spread.
3. Distribution Shape (Skewness):
- Skewness indicates whether the data is symmetric, positively skewed (skewed to the right), or negatively skewed (skewed to the left).
Given the data and calculated values:
### Brand A:
- Mean (average): 20.85
- Standard Deviation: 2.013
- Median: 21.5
- Interquartile Range: 3.25
- Skewness: -0.571 (slightly negatively skewed)
### Brand B:
- Mean (average): 17.1
- Standard Deviation: 3.463
- Median: 18.25
- Interquartile Range: 5.25
- Skewness: -0.576 (slightly negatively skewed)
From the skewness values:
- Both Brand A and Brand B have negative skewness values (close to -0.571 and -0.576 respectively), indicating that both distributions are slightly skewed to the left.
### Conclusion:
Since both Brand A and Brand B distributions are slightly skewed and not perfectly symmetric, the interquartile range (IQR) is more robust against skewness and outliers. The interquartile range provides a better measure for variability in this case.
Therefore, the best measure of variability to use to compare the data is the interquartile range (IQR) because both distributions are skewed left.
This means the correct statement is:
"Both distributions are skewed left, so the interquartile range is the best measure to compare variability."
