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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)
Responses

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 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. 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 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

First, let's calculate the mean absolute deviation (MAD) for the number of items Erica sold over the 8 days.

  1. Calculate the mean of the sales data.

    • Sales data: 32, 56, 19, 8, 19, 58, 34, 19
    • Mean = (32 + 56 + 19 + 8 + 19 + 58 + 34 + 19) / 8
    • Mean = 251 / 8 = 31.375

  2. Calculate the absolute deviations from the mean for each day's sales:

    • |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

  3. Sum the absolute deviations:

    • Total = 0.625 + 24.625 + 12.375 + 23.375 + 12.375 + 26.625 + 2.625 + 12.375
    • Total = 112.625

  4. Calculate the mean absolute deviation:

    • MAD = Total absolute deviation / Number of days
    • MAD = 112.625 / 8 ≈ 14.0781250

We round this to approximately 14.1.

The closest matching response, based on the calculation above, would be:

"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."

This response accurately describes the spread of the number of items sold.