Question

sixth grade > jj.6 calculate mean absolute deviation juv
alana made beaded necklaces in art class to sell for charity. the 5 necklaces used:
30 beads 65 beads 42 beads 57 beads 14 beads
what was the mean absolute deviation of the numbers of beads used?
if the answer is a decimal, round it to the nearest tenth.
mean absolute deviation (mad): ______ beads

Explanation:

Step1: Calculate the mean

First, find the sum of the data values, then divide by the number of values.
$$\text{Mean} = \frac{30 + 65 + 42 + 57 + 14}{5} = \frac{208}{5} = 41.6$$

Step2: Find absolute deviations

Calculate the absolute difference between each data value and the mean.
$|30 - 41.6| = 11.6$
$|65 - 41.6| = 23.4$
$|42 - 41.6| = 0.4$
$|57 - 41.6| = 15.4$
$|14 - 41.6| = 27.6$

Step3: Calculate the MAD

Find the mean of the absolute deviations.
$$\text{MAD} = \frac{11.6 + 23.4 + 0.4 + 15.4 + 27.6}{5} = \frac{78.4}{5} = 15.68$$

Step4: Round to nearest tenth

Round the calculated MAD to one decimal place.
$15.68 \approx 15.7$

Answer:

15.7 beads