Question

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Answer 1

Answer:

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".

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

$Median=\frac{(\frac{n}{2})th+(\frac{n}{2}+1)th}{2}=\frac{48+52}{2}=50$

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

$Median=\frac{(\frac{n}{2})th+(\frac{n}{2}+1)th}{2}=\frac{43+45}{2}=44$

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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