Question

1. the values 6, 8, 12, and 14 have an average of 10. what is the average deviation? 0 12 0 3 0 3.65 2) the values 3, 5, 13 and 19 have an average of 10. what is the average deviation? 0 3 0 6 3) the values 3, 4, 6, 10, and 12 have an average of 7. what is the average deviation? 0 3.2 0 4

Explanation:

Step1: Recall average - deviation formula

The average deviation from the mean is calculated as $\frac{\sum_{i = 1}^{n}|x_{i}-\bar{x}|}{n}$, where $x_{i}$ are the data - points, $\bar{x}$ is the mean, and $n$ is the number of data - points.

Problem 1

• First, find the mean $\bar{x}$ of the data set $\{6,8,12,14\}$.
• $\bar{x}=\frac{6 + 8+12+14}{4}=\frac{40}{4}=10$.
• Then, find the absolute differences from the mean:
• $|6 - 10|=4$, $|8 - 10|=2$, $|12 - 10|=2$, $|14 - 10|=4$.
• The sum of the absolute differences is $4 + 2+2+4 = 12$.
• The average deviation is $\frac{12}{4}=3$.

Problem 2

• The mean $\bar{x}$ of the data set $\{3,5,13,19\}$ is $\bar{x}=\frac{3 + 5+13+19}{4}=\frac{40}{4}=10$.
• Find the absolute differences from the mean:
• $|3 - 10|=7$, $|5 - 10|=5$, $|13 - 10|=3$, $|19 - 10|=9$.
• The sum of the absolute differences is $7 + 5+3+9 = 24$.
• The average deviation is $\frac{24}{4}=6$.

Problem 3

• The mean $\bar{x}$ of the data set $\{3,4,6,10,12\}$ is $\bar{x}=\frac{3 + 4+6+10+12}{5}=\frac{35}{5}=7$.
• Find the absolute differences from the mean:
• $|3 - 7|=4$, $|4 - 7|=3$, $|6 - 7|=1$, $|10 - 7|=3$, $|12 - 7|=5$.
• The sum of the absolute differences is $4+3 + 1+3+5 = 16$.
• The average deviation is $\frac{16}{5}=3.2$.

Answer:

1. 3
2. 6
3. 3.2