Question

the data set below has 6 values. find the mean absolute deviation for the data set. if necessary, round your answer to the nearest hundredth. 8, 14, 7, 22, 10, 23 send data to calculator mean absolute deviation: 3.2 note selecting \i dont know\ will impact your final result. try solving the problem, even if youre not 100% sure about the answer. got it

Explanation:

Step1: Calculate the mean of the data set.

The formula for the mean $\bar{x}$ of a data set with $n$ values $x_1, x_2, \dots, x_n$ is $\bar{x}=\frac{\sum_{i = 1}^{n}x_i}{n}$.
Here, $n = 6$, and the data values are $8,14,7,22,10,23$.
First, find the sum: $8 + 14+7 + 22+10 + 23=\sum_{i = 1}^{6}x_i$.
$8+14 = 22$; $22 + 7=29$; $29+22 = 51$; $51+10 = 61$; $61+23 = 84$.
Then, the mean $\bar{x}=\frac{84}{6}=14$.

Step2: Find the absolute deviation of each data point from the mean.

The absolute deviation of a data point $x_i$ from the mean $\bar{x}$ is $|x_i-\bar{x}|$.

• For $x_1 = 8$: $|8 - 14|=|-6| = 6$.
• For $x_2 = 14$: $|14 - 14|=|0| = 0$.
• For $x_3 = 7$: $|7 - 14|=|-7| = 7$.
• For $x_4 = 22$: $|22 - 14|=|8| = 8$.
• For $x_5 = 10$: $|10 - 14|=|-4| = 4$.
• For $x_6 = 23$: $|23 - 14|=|9| = 9$.

Step3: Calculate the mean of these absolute deviations.

The formula for the mean absolute deviation (MAD) is $MAD=\frac{\sum_{i = 1}^{n}|x_i-\bar{x}|}{n}$.
First, find the sum of the absolute deviations: $6 + 0+7 + 8+4 + 9=\sum_{i = 1}^{6}|x_i - \bar{x}|$.
$6+0 = 6$; $6 + 7=13$; $13+8 = 21$; $21+4 = 25$; $25+9 = 34$.
Then, $MAD=\frac{34}{6}\approx5.67$ (rounded to the nearest hundredth).

Answer:

$5.67$