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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 shopping time for each group, we start by calculating the total time spent by each group and then dividing by the number of members in each group.

Group A times: 18, 20, 46, 34, 58, 31, 41

  1. Calculate the total time for Group A: \[ 18 + 20 + 46 + 34 + 58 + 31 + 41 = 248 \]

  2. Count the number of members in Group A: \[ 7 \]

  3. Calculate the mean for Group A: \[ \text{Mean of Group A} = \frac{248}{7} \approx 35.4 \text{ minutes} \]

Group B times: 15, 21, 32, 42, 29, 57, 39

  1. Calculate the total time for Group B: \[ 15 + 21 + 32 + 42 + 29 + 57 + 39 = 235 \]

  2. Count the number of members in Group B: \[ 7 \]

  3. Calculate the mean for Group B: \[ \text{Mean of Group B} = \frac{235}{7} \approx 33.6 \text{ minutes} \]

Difference in the mean times: \[ \text{Difference} = \text{Mean of Group A} - \text{Mean of Group B} = 35.4 - 33.6 = 1.8 \text{ minutes} \]

Final 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.