Question

rin incorrectly calculated the mean absolute deviation for the data set 25,25,31,36,38.her work is shown here. 1. find the mean. mean = (25 + 25 + 31 + 36 + 38)/5 = 155/5 = 31 2. find each absolute deviation. absolute deviations:6,6,0,5,7 3. find the mean absolute deviation. mad = (6 + 0 + 5 + 7)/4 = 18/4 = 4.5 in which step did rin make an error?

Explanation:

Step1: Analyze Step 1 (Mean Calculation)

Sum of data: \(25 + 25 + 31 + 36 + 38 = 155\), mean: \(\frac{155}{5}=31\). This step is correct.

Step2: Analyze Step 2 (Absolute Deviations)

Absolute deviation is \(|x - \text{mean}|\). For \(25\): \(|25 - 31| = 6\) (two times, correct), \(31\): \(|31 - 31| = 0\) (correct), \(36\): \(|36 - 31| = 5\) (correct), \(38\): \(|38 - 31| = 7\) (correct). This step is correct.

Step3: Analyze Step 3 (MAD Calculation)

Mean Absolute Deviation (MAD) is the mean of all absolute deviations. There are 5 data points, so we should divide by 5, not 4. The sum of absolute deviations is \(6 + 6 + 0 + 5 + 7 = 24\), so \(MAD=\frac{24}{5}=4.8\), but Rin divided by 4. So error is in Step 3.

Answer:

Step 3 (Find the mean absolute deviation)