Answer:
As both data distribution are not symmetric for both Coffee Shop A and Coffee Shop B. Therefore, it is appropriate to mention the centers of distribution in terms of median for both coffee shops.
Hence, option B should be correct option.
Step-by-step explanation:
Calculation for Coffee Shop A:
The data distribution for shop A:
[tex]12, 52, 57, 33, 51, 15, 46, 45[/tex]
Arrange the data in ascending order.
[tex]12, 15, 33, 45, 46, 51, 52, 57[/tex]
Mean for shop A:
[tex]Mean=\frac{12+15+33+45+46+51+52+57}{8}=38.875[/tex]
[tex]Median=\frac{(\frac{n}{2})th+(\frac{n}{2}+1)th}{2}=\frac{45+46}{2}=45.5[/tex]
As Mean and Median are not close. Hence, data distribution is not symmetric for Coffee Shop A.
Calculation for Coffee Shop B:
The data distribution for shop B:
[tex]17, 16, 36, 35, 12, 9, 34, 15[/tex]
Arrange the data in ascending order.
[tex]9, 12, 15, 16, 17, 34, 35, 36[/tex]
Mean for shop B:
[tex]Mean=\frac{9+12+15+16+17+34+35+36}{8}=21.75[/tex]
[tex]Median=\frac{(\frac{n}{2})th+(\frac{n}{2}+1)th}{2}=\frac{16+17}{2}=16.5[/tex]
As Mean and Median are not close. Hence, data distribution is not symmetric for Coffee Shop B.
As both data distribution are not symmetric for both Coffee Shop A and Coffee Shop B.
Therefore, it is appropriate to mention the centers of distribution in terms of median for both coffee shops.
Hence, option B should be correct option.
Keywords: data distribution, mean, median
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