To determine the best measure of variability to use to compare the data for the battery lives of Brand A and Brand B, let's follow these steps:
1. Calculating the mean:
- For Brand A: The mean battery life is [tex]\( \overline{X}_A = 20.85 \)[/tex] hours.
- For Brand B: The mean battery life is [tex]\( \overline{X}_B = 17.1 \)[/tex] hours.
2. Calculating the median:
- For Brand A: The median battery life is [tex]\( \text{Median}_A = 21.5 \)[/tex] hours.
- For Brand B: The median battery life is [tex]\( \text{Median}_B = 18.25 \)[/tex] hours.
3. Determining skewness:
- For Brand A: The skewness can be approximated by [tex]\( \text{Skewness}_A = | \overline{X}_A - \text{Median}_A | = | 20.85 - 21.5 | = 0.65 \)[/tex].
- For Brand B: The skewness can be approximated by [tex]\( \text{Skewness}_B = | \overline{X}_B - \text{Median}_B | = | 17.1 - 18.25 | = 1.15 \)[/tex].
4. Evaluating the symmetry:
- Since both skewness values for Brand A (0.65) and Brand B (1.15) are not close to 0, we can infer that both distributions are skewed.
5. Considering the best measure of variability:
- When distributions are symmetric, the standard deviation is often used to represent the variability.
- When distributions are skewed, the interquartile range (IQR) is a better measure of variability because it is not affected by extreme values or skewness.
Given that:
- The skewness for Brand A is 0.65.
- The skewness for Brand B is 1.15.
- These values indicate that both distributions are skewed.
Thus, the best measure of variability to compare the data for these two brands is the interquartile range (IQR).
Conclusion:
"Both distributions are skewed left, so the interquartile range is the best measure to compare variability."
