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Erica sells pottery at fairs every summer. She records the number of items she sells each day The number of items she sells each day over the course of 8 days is 32, 56, 19, 8, 19, 58, 34, 19 Describe the spread of the number of items Erica sold each day using the mean absolute deviation. (1 point)

The mean absolute deviation is approximately 50. The difference between the maximum number of items Erica sold in a day and the minimum number of items Erica sold in a day was 50

The mean absolute deviation is approximately 14.4. On average, the number of items Erica sold each day is about 14.4 items from the mean.

The mean absolute deviation is approximately 14.4. Erica sold within 14.4 items of the mean each day

The mean absolute deviation is approximately 30.6. Erica sold around 31 items each day.

1 answer

To calculate the Mean Absolute Deviation (MAD), we first need to find the mean of the data set and then the absolute deviations from that mean.

  1. Data Set: 32, 56, 19, 8, 19, 58, 34, 19

  2. Calculate the Mean:

    • First, sum the values: \(32 + 56 + 19 + 8 + 19 + 58 + 34 + 19 = 251\)
    • Then divide by the number of days (8): \[ \text{Mean} = \frac{251}{8} \approx 31.375 \]

  3. Calculate the Absolute Deviations:

    • Now we find the absolute deviations from the mean:
      • |32 - 31.375| = 0.625
      • |56 - 31.375| = 24.625
      • |19 - 31.375| = 12.375
      • |8 - 31.375| = 23.375
      • |19 - 31.375| = 12.375
      • |58 - 31.375| = 26.625
      • |34 - 31.375| = 2.625
      • |19 - 31.375| = 12.375

  4. Calculate the Mean Absolute Deviation:

    • Sum these absolute deviations: \[ 0.625 + 24.625 + 12.375 + 23.375 + 12.375 + 26.625 + 2.625 + 12.375 = 115.125 \]
    • Then divide by the number of values (8): \[ \text{MAD} \approx \frac{115.125}{8} \approx 14.39 \]

  5. Conclusion: The mean absolute deviation is approximately 14.4. Thus, the correct statement is:

"The mean absolute deviation is approximately 14.4. On average, the number of items Erica sold each day is about 14.4 items from the mean."