Question

a construction worker checked the number of screws needed to complete 7 jobs. he counted:
45 screws 13 screws 25 screws 59 screws 30 screws 24 screws 63 screws
what was the mean absolute deviation of the numbers of screws needed?
if the answer is a decimal, round it to the nearest tenth.
mean absolute deviation (mad): _______ screws

Explanation:

Step1: Calculate the mean

First, sum all values then divide by count.
$$\text{Mean} = \frac{45 + 13 + 25 + 59 + 30 + 24 + 63}{7} = \frac{259}{7} = 37$$

Step2: Find absolute deviations

Subtract mean from each value, take absolute value.
$|45-37|=8$, $|13-37|=24$, $|25-37|=12$, $|59-37|=22$, $|30-37|=7$, $|24-37|=13$, $|63-37|=26$

Step3: Calculate MAD of deviations

Sum absolute deviations, divide by count.
$$\text{MAD} = \frac{8 + 24 + 12 + 22 + 7 + 13 + 26}{7} = \frac{112}{7} = 16.0$$

Answer:

16.0 screws