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The number of lattes sold daily by two coffee shops is shown in the table.Shop A Shop B55 3652 4050 3447 3951 4448 4153 4053 38Based on these data, is it better to describe the centers of distribution in terms of the mean or the median? Explain. (1 point)Mean for both coffee shops because the data distribution is symmetricMedian for both coffee shops because the data distribution is not symmetricMean for shop B because the data distribution is symmetric; median for shop A because the data distribution is not symmetricMean for shop A because the data distribution is symmetric; median for shop B because the data distribution is not symmetric

Question

The number of lattes sold daily by two coffee shops is shown in the table.Shop A Shop B55 3652 4050 3447 3951 4448 4153 4053 38Based on these data, is it better to describe the centers of distribution in terms of the mean or the median? Explain. (1 point)Mean for both coffee shops because the data distribution is symmetricMedian for both coffee shops because the data distribution is not symmetricMean for shop B because the data distribution is symmetric; median for shop A because the data distribution is not symmetricMean for shop A because the data distribution is symmetric; median for shop B because the data distribution is not symmetric

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Solution

To answer this question, we first need to determine whether the data distribution is symmetric or not. Symmetric distribution means that the values are evenly distributed around the center. If the distribution is not symmetric (i.e., it is skewed), the median is a better measure of center because it is not affected by extreme values.

Let's calculate the mean and median for both shops:

Shop A: Mean = (55+52+50+47+51+48+53+53)/8 = 51.125 The numbers in ascending order are: 47, 48, 50, 51, 52, 53, 53, 55. The median is the average of the two middle numbers, which is (51+52)/2 = 51.5

Shop B: Mean = (36+40+34+39+44+41+40+38)/8 = 39 The numbers in ascending order are: 34, 36, 38, 39, 40, 40, 41, 44. The median is the average of the two middle numbers, which is (39+40)/2 = 39.5

Looking at the data, it seems that the distribution is fairly symmetric for both shops, as the mean and median are very close to each other. Therefore, it would be appropriate to describe the centers of distribution in terms of the mean for both coffee shops.

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