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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 times for Group A and Group B, we need to calculate the average time spent by each group.

Step 1: Calculate the mean for Group A.

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

  1. Calculate the sum of Group A's times: \( 18 + 20 + 46 + 34 + 58 + 31 + 41 = 248 \)

  2. Count the number of entries in Group A: \( 7 \)

  3. Calculate the mean: \[ \text{Mean}_A = \frac{\text{Sum of Group A}}{\text{Number of entries}} = \frac{248}{7} \approx 35.4 \]

Step 2: Calculate the mean for Group B.

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

  1. Calculate the sum of Group B's times: \( 15 + 21 + 32 + 42 + 29 + 57 + 39 = 235 \)

  2. Count the number of entries in Group B: \( 7 \)

  3. Calculate the mean: \[ \text{Mean}_B = \frac{\text{Sum of Group B}}{\text{Number of entries}} = \frac{235}{7} \approx 33.6 \]

Step 3: Determine the difference in mean times.

  1. Calculate the difference: \[ \text{Difference} = \text{Mean}_A - \text{Mean}_B = 35.4 - 33.6 = 1.8 \]

Final Answers:

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