Question

five friends recorded the number of action figures each friend has. the following is the dataset they recorded: {7, 9, 10, 11, 11}. which of the following correctly calculates the average deviation from the mean number of action figures? (1 point)
the average deviation from the mean is 1.28.
the average deviation from the mean is 6.4.
the average deviation from the mean is 0.16.
the average deviation from the mean is 9.6.

Explanation:

Step1: Calculate the mean

The formula for the mean $\bar{x}$ of a data set $\{x_1,x_2,\cdots,x_n\}$ is $\bar{x}=\frac{\sum_{i = 1}^{n}x_i}{n}$.
For the data set $\{7,9,10,11,11\}$, $n = 5$, and $\sum_{i=1}^{5}x_i=7 + 9+10 + 11+11=48$.
So, $\bar{x}=\frac{48}{5}=9.6$.

Step2: Calculate the absolute deviations

The absolute deviation of each data point $x_i$ from the mean $\bar{x}$ is $|x_i-\bar{x}|$.
For $x_1 = 7$: $|7 - 9.6|=2.6$; for $x_2 = 9$: $|9 - 9.6|=0.6$; for $x_3 = 10$: $|10 - 9.6|=0.4$; for $x_4 = 11$: $|11 - 9.6|=1.4$; for $x_5 = 11$: $|11 - 9.6|=1.4$.

Step3: Calculate the average deviation

The formula for the average deviation (also known as the mean - absolute - deviation) is $\text{Average Deviation}=\frac{\sum_{i = 1}^{n}|x_i-\bar{x}|}{n}$.
$\sum_{i = 1}^{5}|x_i-\bar{x}|=2.6+0.6 + 0.4+1.4+1.4=6.4$.
Then, $\text{Average Deviation}=\frac{6.4}{5}=1.28$.

Answer:

The average deviation from the mean is 1.28.