Question

The owner of a bagel shop recorded the number of bagels sold each day for a week. Her results were 699, 751, 810, 842, 923, 1,061, 1,214. Describe the spread of number of bagels sold each day using the mean absolute deviation.

135.4
142.3
163.2
900.1

Answer 1

To calculate the mean absolute deviation (MAD), we first need to find the mean (average) number of bagels sold over the week, and then we will find the absolute deviations from that mean.

1. **Calculate the Mean:**
\[
\text{Mean} = \frac{\text{Sum of values}}{\text{Number of values}}
\]

The sum of the bagels sold:
\[
699 + 751 + 810 + 842 + 923 + 1,061 + 1,214 = 5,510
\]

The number of days (values) is 7.

Now, calculating the mean:
\[
\text{Mean} = \frac{5,510}{7} \approx 787.14
\]

2. **Calculate the Absolute Deviations:**
Now we calculate the absolute deviation of each day's sales from the mean:
\[
|699 - 787.14| \approx 88.14
\]
\[
|751 - 787.14| \approx 36.14
\]
\[
|810 - 787.14| \approx 22.86
\]
\[
|842 - 787.14| \approx 54.86
\]
\[
|923 - 787.14| \approx 135.86
\]
\[
|1,061 - 787.14| \approx 273.86
\]
\[
|1,214 - 787.14| \approx 426.86
\]

3. **Calculate the Mean Absolute Deviation:**
Now, we calculate the mean of these absolute deviations:
\[
\text{MAD} = \frac{88.14 + 36.14 + 22.86 + 54.86 + 135.86 + 273.86 + 426.86}{7}
\]
\[
\text{MAD} \approx \frac{1,037.6}{7} \approx 148.23
\]

Given your options (135.4, 142.3, 163.2, 900.1), the nearest value to our computed mean absolute deviation (148.23) is not listed exactly, but among the given choices the closest appears to be **142.3**. Thus, the answer is:

**142.3**.