Question

in the data set below, what is the mean absolute deviation?
2 9 3 2 5 2 5
if the answer is a decimal, round it to the nearest tenth.
mean absolute deviation (mad):
submit

Explanation:

Step1: Calculate the dataset mean

First, sum all values: $2 + 9 + 3 + 2 + 5 + 2 + 5 = 28$
Then divide by the number of values ($n=7$):
$\text{Mean} = \frac{28}{7} = 4$

Step2: Find absolute deviations

Subtract the mean from each value and take the absolute value:
$|2-4|=2$, $|9-4|=5$, $|3-4|=1$, $|2-4|=2$, $|5-4|=1$, $|2-4|=2$, $|5-4|=1$

Step3: Calculate MAD of deviations

Sum the absolute deviations: $2 + 5 + 1 + 2 + 1 + 2 + 1 = 14$
Divide by the number of values:
$\text{MAD} = \frac{14}{7} = 2$
Wait, correction: Wait no, recalculate sum of absolute deviations: 2+5=7, +1=8, +2=10, +1=11, +2=13, +1=14. $\frac{14}{7}=2$. Wait, no, wait original dataset: 2,9,3,2,5,2,5. Count is 7. Mean is 4. Absolute deviations: 2,5,1,2,1,2,1. Sum is 14. 14/7=2. But wait, maybe miscalculation? Wait 2+5 is 7, plus 1 is 8, plus 2 is 10, plus 1 is 11, plus 2 is 13, plus 1 is 14. 14 divided by 7 is 2. So the MAD is 2.0, rounded to nearest tenth is 2.0.

Wait, correction:

Step1: Compute dataset mean

Sum: $2+9+3+2+5+2+5=28$
$\text{Mean} = \frac{28}{7}=4$

Step2: Compute absolute deviations

$|2-4|=2$, $|9-4|=5$, $|3-4|=1$, $|2-4|=2$, $|5-4|=1$, $|2-4|=2$, $|5-4|=1$

Step3: Compute MAD

Sum of deviations: $2+5+1+2+1+2+1=14$
$\text{MAD} = \frac{14}{7}=2.0$

Final Answer:

2.0

Answer:

1.9