PLEASE HURRY!!!!!!
The number of lattes sold daily by two coffee shops is shown in the table.
Shop A Shop B
55 45
52 42
56 57
48 48
57 11
30 10
45 46
41 43
Based on these data, is it better to describe the centers of distribution in terms of the mean or the median? Explain.

1) Mean for both coffee shops because the data distribution is symmetric
2) Median for both coffee shops because the data distribution is not symmetric
3) Mean for shop B because the data distribution is symmetric; median for shop A because the data distribution is not symmetric
4) Mean for shop A because the data distribution is symmetric; median for shop B because the data distribution is not symmetric

Therefore, option 4) is correct which states that "Mean for shop A because the data distribution is symmetric; median for shop B because the data distribution is not symmetric".

Step-by-step explanation:

Calculation for Coffee Shop A:

The data distribution for shop A:

55, 52, 56, 48, 57, 30, 45, 41

Arrange the data in ascending order.

30, 41, 45, 48, 52, 55, 56, 57

Mean for shop A:

Mean = (30 + 41 + 45 + 48 + 52 + 55 + 56 + 57)/8 = 48

[tex]Median=\frac{(\frac{n}{2})th+(\frac{n}{2}+1)th}{2}=\frac{48+52}{2}=50[/tex]

As Mean and Median are close. Hence, data distribution is symmetric for Coffee Shop A.

Calculation for Coffee Shop B:

The data distribution for shop B:

45, 42, 57, 48, 11, 10, 46, 43

Arrange the data in ascending order.

10, 11, 42, 43, 45, 46, 48, 57

Mean for shop B:

Mean = (10 + 11 + 42 + 43 + 45 + 46 + 48 + 57)/8 = 37.75

[tex]Median=\frac{(\frac{n}{2})th+(\frac{n}{2}+1)th}{2}=\frac{43+45}{2}=44[/tex]

As Mean and Median are not close. Hence, data distribution is not symmetric for Coffee Shop B.

As data distribution is symmetric for Coffee Shop A and data distribution is not symmetric for Coffee Shop B.

Therefore, option 4) is correct which states that "Mean for shop A because the data distribution is symmetric; median for shop B because the data distribution is not symmetric".

Keywords: data distribution, median , mean

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