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Use the table to answer the question.

Comparison of Shopping Time Between Group A and Group B
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 first need to calculate the sum of the times for each group and then divide by the number of values in each group.

Group A:

Times: 18, 20, 46, 34, 58, 31, 41

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

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

Group B:

Times: 15, 21, 32, 42, 29, 57, 39

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

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

Determine the difference in mean times:

The difference between the mean times for Group A and Group B is: \[ \text{Difference} = \text{Mean A} - \text{Mean B} = 35.4 - 33.6 = 1.8 \text{ minutes} \]

Summary:

  • 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 of Group A and Group B differ by 1.8 minutes.