To determine whether to describe the centers of distribution in terms of mean or median for the two bakeries, we need to consider the symmetry of the data distributions. Typically, if the data distribution is symmetric, the mean is a suitable measure of central tendency because it reflects the central point of symmetrical data accurately. If the data distribution is not symmetric (skewed), the median is preferred as it better represents the center of the data by not being influenced by outliers.
Given the data:
- Bakery A: [60, 52, 50, 48, 53, 47, 52, 60]
- Bakery B: [34, 40, 36, 38, 41, 44, 40, 39]
First, let's consider the measures of central tendency for each bakery:
1. Bakery A:
- Compute the mean and median for Bakery A.
- Mean = (60 + 52 + 50 + 48 + 53 + 47 + 52 + 60) / 8
- To verify symmetry, compare the mean and median.
2. Bakery B:
- Compute the mean and median for Bakery B.
- Mean = (34 + 40 + 36 + 38 + 41 + 44 + 40 + 39) / 8
- To verify symmetry, compare the mean and median.
We found that both the mean and median values for Bakery A and Bakery B do not match (not symmetric). Therefore:
- Bakery A does not have symmetry.
- Bakery B does not have symmetry.
Therefore, the best option would be:
d. Median for both bakeries because the data is not symmetric.
