Questions: Question 7 1 pts ( 05.02 MC ) The number of lattes sold daily by two coffee shops is shown in the table. Shop A Shop B ------ 55 36 52 40 50 34 47 39 51 44 48 41 53 40 53 38 Based on these data, is it better to describe the centers of distribution in terms of the mean or the median? Explain. - Mean for both coffee shops because the data distribution is symmetric - Median for both coffee shops because the data distribution is not symmetric - Mean for shop B because the data distribution is symmetric; median for shop A because the data distribution is not symmetric - Mean for shop A because the data distribution is symmetric: median for shop B because the data distribution is not symmetric

Question 7
1 pts
( 05.02 MC )
The number of lattes sold daily by two coffee shops is shown in the table.

Shop A  Shop B
------
55  36
52  40
50  34
47  39
51  44
48  41
53  40
53  38

Based on these data, is it better to describe the centers of distribution in terms of the mean or the median? Explain.
- Mean for both coffee shops because the data distribution is symmetric
- Median for both coffee shops because the data distribution is not symmetric
- Mean for shop B because the data distribution is symmetric; median for shop A because the data distribution is not symmetric
- Mean for shop A because the data distribution is symmetric: median for shop B because the data distribution is not symmetric
Transcript text: Question 7 1 pts ( 05.02 MC ) The number of lattes sold daily by two coffee shops is shown in the table. \begin{tabular}{|l|l|} \hline Shop A & Shop B \\ \hline 55 & 36 \\ \hline 52 & 40 \\ \hline 50 & 34 \\ \hline 47 & 39 \\ \hline 51 & 44 \\ \hline 48 & 41 \\ \hline 53 & 40 \\ \hline 53 & 38 \\ \hline \end{tabular} Based on these data, is it better to describe the centers of distribution in terms of the mean or the median? Explain. Mean for both coffee shops because the data distribution is symmetric Median for both coffee shops because the data distribution is not symmetric Mean for shop $B$ because the data distribution is symmetric; median for shop $A$ because the data distribution is not symmetric Mean 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

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Solution Steps

Step 1: Calculate the Mean for Shop A

The mean for Shop A is calculated as follows:

\[ \mu_A = \frac{\sum_{i=1}^N x_i}{N} = \frac{409}{8} = 51.12 \]

Step 2: Calculate the Median for Shop A

The sorted data for Shop A is:

\[ [47, 48, 50, 51, 52, 53, 53, 55] \]

To find the median, we use the formula for the rank:

\[ \text{Rank} = Q \times (N + 1) = 0.5 \times (8 + 1) = 4.5 \]

The median is then calculated using the averaging formula:

\[ Q = \frac{X_{\text{lower}} + X_{\text{upper}}}{2} = \frac{51 + 52}{2} = 51.5 \]

Step 3: Calculate the Mean for Shop B

The mean for Shop B is calculated as follows:

\[ \mu_B = \frac{\sum_{i=1}^N x_i}{N} = \frac{312}{8} = 39.0 \]

Step 4: Calculate the Median for Shop B

The sorted data for Shop B is:

\[ [34, 36, 38, 39, 40, 40, 41, 44] \]

To find the median, we again use the formula for the rank:

\[ \text{Rank} = Q \times (N + 1) = 0.5 \times (8 + 1) = 4.5 \]

The median is calculated using the averaging formula:

\[ Q = \frac{X_{\text{lower}} + X_{\text{upper}}}{2} = \frac{39 + 40}{2} = 39.5 \]

Step 5: Assess the Symmetry of the Data Distribution

For Shop A:

  • Mean: \( \mu_A = 51.12 \)
  • Median: \( Q_A = 51.5 \)

Since \( \mu_A \neq Q_A \), the data distribution for Shop A is not symmetric.

For Shop B:

  • Mean: \( \mu_B = 39.0 \)
  • Median: \( Q_B = 39.5 \)

Since \( \mu_B \neq Q_B \), the data distribution for Shop B is not symmetric.

Final Answer

Based on the calculations, the appropriate measures of central tendency are:

  • Median for both coffee shops because the data distribution is not symmetric.

Thus, the answer is:

\(\boxed{\text{Median for both coffee shops because the data distribution is not symmetric.}}\)

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