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Use the table to answer the question.

This table displays the shopping time taken by Group A and Group B for comparison.
Group A 18 20 46 34 58 31 41
Group B 15 21 32 42 29 57 39The table shows the times, in minutes, spent shopping by two different groups. First find the mean times each group spent shopping. Then determine the difference in the mean times. Round your answers to one decimal place.(2 points)
The mean time Group A spent shopping is
minutes.
The mean time Group B spent shopping is
minutes.
The mean times Group A and Group B spent shopping differ by
minutes.
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1 answer

To calculate the mean shopping time for each group, we follow these steps:

  1. Calculate the mean for Group A:

    • Sum of Group A's times: \( 18 + 20 + 46 + 34 + 58 + 31 + 41 = 248 \)
    • Number of members in Group A: \( 7 \)
    • Mean for Group A: \[ \text{Mean}_A = \frac{248}{7} \approx 35.4 \]

  2. Calculate the mean for Group B:

    • Sum of Group B's times: \( 15 + 21 + 32 + 42 + 29 + 57 + 39 = 235 \)
    • Number of members in Group B: \( 7 \)
    • Mean for Group B: \[ \text{Mean}_B = \frac{235}{7} \approx 33.6 \]

  3. Determine the difference in mean times: \[ \text{Difference} = \text{Mean}_A - \text{Mean}_B = 35.4 - 33.6 = 1.8 \]

Now, summarizing the results:

  • The mean time Group A spent shopping is 35.4 minutes.
  • The mean time Group B spent shopping is 33.6 minutes.
  • The mean times Group A and Group B spent shopping differ by 1.8 minutes.