To determine the most appropriate measure of variability to compare the battery life data for Brand A and Brand B, we need to analyze the distribution of the data for both brands considering their symmetry.
The four options given for the measure are:
1. Only Brand A data is symmetric, so standard deviation is the best measure to compare variability.
2. Only Brand B data is symmetric, so the median is the best measure to compare variability.
3. Both distributions are symmetric, so the mean is the best measure to compare variability.
4. Both distributions are skewed left, so the interquartile range is the best measure to compare variability.
Step-by-Step Analysis:
1. Identify Symmetry:
- First, we need to assess the symmetry of the data for both Brand A and Brand B.
- If a dataset is symmetric, its mean and median are approximately equal, and standard deviation becomes a reliable measure of variability.
- For a skewed dataset, the median and interquartile range would better describe the data distribution.
2. Data Review:
- For Brand A: [22.5, 17.0, 21.0, 23.0, 22.0, 18.5, 22.5, 20.0, 19.0, 23.0]
- For Brand B: [20.0, 19.5, 20.5, 16.5, 14.0, 17.0, 11.0, 19.5, 21.0, 12.0]
3. Analyze Symmetry:
- Symmetry analysis involves comparing the mean and median of the datasets.
- Calculate the skewness for both datasets to understand if each dataset is symmetric or skewed.
- If the skewness is close to 0, it indicates symmetry.
- If the skewness is significantly different from 0, it indicates the data is skewed.
4. Given Result Interpretation:
- The result indicates that both distributions are symmetric.
- For symmetric data distributions, the mean is the best measure for central tendency and typically, the standard deviation is a good measure of variability.
Conclusion:
Given that both distributions are symmetric, the most appropriate measure of variability to compare the data is:
Both distributions are symmetric, so the mean is the best measure to compare variability.
