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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

To find the mean absolute deviation (MAD), we will first calculate the mean number of items sold over the 8 days, then the absolute deviations from the mean, and finally the average of those absolute deviations.

  1. Finding the mean:

    • Items sold: \(32, 56, 19, 8, 19, 58, 34, 19\)
    • Total items sold = \(32 + 56 + 19 + 8 + 19 + 58 + 34 + 19 = 251\)
    • Number of days = \(8\)
    • Mean = \(\frac{251}{8} \approx 31.375\)

  2. Finding 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

  3. Calculating the mean absolute deviation:

    • Sum of absolute deviations = \(0.625 + 24.625 + 12.375 + 23.375 + 12.375 + 26.625 + 2.625 + 12.375 = 112.125\)
    • MAD = \(\frac{112.125}{8} \approx 14.015625\)

Thus, the mean absolute deviation (MAD) is approximately 14.0. Rounding it gives about 14.4.

So, the correct statement regarding the spread of the number of items Erica sold each day using mean absolute deviation 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.