Question

these values have an average of 8. what is the average distance of those values from that average of 8? 2 4 8 12 14 ex: 1 1 2 check next

Explanation:

Step1: Recall average formula

The formula for the average (arithmetic - mean) of a set of numbers $x_1,x_2,\cdots,x_n$ is $\bar{x}=\frac{\sum_{i = 1}^{n}x_i}{n}$. Here, $n = 5$, and $x_1=2,x_2 = 4,x_3=8,x_4=12,x_5=14$. First, find the sum of the numbers: $\sum_{i=1}^{5}x_i=2 + 4+8+12+14=40$.

Step2: Calculate the average

Using the average formula $\bar{x}=\frac{\sum_{i = 1}^{5}x_i}{5}=\frac{40}{5}=8$.

Step3: Calculate the absolute - deviation from the average for each number

For $x_1 = 2$: $|2 - 8|=6$; for $x_2 = 4$: $|4 - 8|=4$; for $x_3=8$: $|8 - 8|=0$; for $x_4=12$: $|12 - 8|=4$; for $x_5=14$: $|14 - 8|=6$.

Step4: Calculate the sum of the absolute - deviations

$\sum_{i = 1}^{5}|x_i - 8|=6 + 4+0+4+6=20$.

Step5: Calculate the average distance from the average

The average distance from the average is $\frac{\sum_{i = 1}^{5}|x_i - 8|}{5}=\frac{20}{5}=4$.

Answer:

4