Question

deviation from the mean practice
complete this assessment to review what youve learned. it will not count toward your grade.
dataset a, {7, 9, 9, 12}, and dataset b, {6, 8, 10, 13}, both have a mean of 9.25. calculate the
average deviation from the mean of each dataset. (1 point)
the average deviation from the mean of dataset a is □. the average deviation from the
mean of dataset b is □.
check answer remaining attempts : 3

Explanation:

Step1: Calculate the mean of dataset A

The formula for the mean \(\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}\). For dataset \(A=\{7,9,9,12\}\), \(n = 4\), \(\sum_{i=1}^{4}x_{i}=7 + 9+9 + 12=37\). So, \(\bar{x}_A=\frac{37}{4}=9.25\)

Step2: Calculate the absolute deviations for dataset A

\(\vert7 - 9.25\vert=2.25\), \(\vert9 - 9.25\vert=0.25\), \(\vert9 - 9.25\vert=0.25\), \(\vert12 - 9.25\vert=2.75\)

Step3: Calculate the average deviation for dataset A

The formula for average deviation is \(\frac{\sum_{i = 1}^{n}\vert x_{i}-\bar{x}\vert}{n}\). \(\sum_{i = 1}^{4}\vert x_{i}-\bar{x}_A\vert=2.25+0.25 + 0.25+2.75 = 5.5\). So, average deviation \(=\frac{5.5}{4}=1.375\)

Step4: Calculate the mean of dataset B

For dataset \(B=\{6,8,10,13\}\), \(n = 4\), \(\sum_{i=1}^{4}x_{i}=6 + 8+10 + 13=37\). So, \(\bar{x}_B=\frac{37}{4}=9.25\)

Step5: Calculate the absolute deviations for dataset B

\(\vert6 - 9.25\vert=3.25\), \(\vert8 - 9.25\vert=1.25\), \(\vert10 - 9.25\vert=0.75\), \(\vert13 - 9.25\vert=3.75\)

Step6: Calculate the average deviation for dataset B

\(\sum_{i = 1}^{4}\vert x_{i}-\bar{x}_B\vert=3.25+1.25 + 0.75+3.75 = 9\). So, average deviation \(=\frac{9}{4}=2.25\)

Answer:

The average deviation from the mean of dataset \(A\) is \(1.375\). The average deviation from the mean of dataset \(B\) is \(2.25\)