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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 39
The 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.

1 answer

To find the mean time for each group, we can follow these steps:

  1. Calculate the mean for Group A:

    • Add all the shopping times for Group A: \( 18 + 20 + 46 + 34 + 58 + 31 + 41 = 248 \)
    • Count the number of entries in Group A: \( 7 \)
    • Calculate the mean: \[ \text{Mean for Group A} = \frac{248}{7} \approx 35.4 \text{ minutes} \]

  2. Calculate the mean for Group B:

    • Add all the shopping times for Group B: \( 15 + 21 + 32 + 42 + 29 + 57 + 39 = 235 \)
    • Count the number of entries in Group B: \( 7 \)
    • Calculate the mean: \[ \text{Mean for Group B} = \frac{235}{7} \approx 33.6 \text{ minutes} \]

  3. Determine the difference in the mean times between Group A and Group B: \[ \text{Difference} = 35.4 - 33.6 = 1.8 \text{ minutes} \]

Now we can fill in the answers:

  • 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.