What is the mean absolute deviation of the data set? Round to the nearest hundredth if necessary.
61, 42, 52, 27, 35, 23
First find median:
61, 42, 52, 27, 35, 23
Step 1: 61 + 42 + 52 + 27 + 35 + 23 = 240
Step 2: Add up amount of numbers: 6
Step 3: Divide total by number amount: 240/6 = 40
Next steps:
2. Find the absolute value of the difference between each data value and the mean: |data value – mean|.
3. Find the sum of the absolute values of the differences.
4. Divide the sum of the absolute values of the differences by the number of data values.
Calculating the mean average helps you determine the deviation from the mean by calculating the difference between the mean and each value. Next, divide the sum of all previously calculated values by the number of deviations added together and the result is the average deviation from the mean.
To find the mean absolute deviation (MAD) of a data set, follow these steps:
1. Calculate the mean (average) of the data set by adding up all the numbers and dividing by the total count.
For this data set:
Mean = (61 + 42 + 52 + 27 + 35 + 23) / 6 = 240 / 6 = 40
2. Find the absolute deviation of each number by subtracting the mean from each value, regardless of whether the difference is positive or negative.
Absolute Deviation = |Value - Mean|
For each value in the data set:
|61 - 40| = 21
|42 - 40| = 2
|52 - 40| = 12
|27 - 40| = 13
|35 - 40| = 5
|23 - 40| = 17
3. Find the average of all the absolute deviations. Add up all the absolute deviations you calculated in step 2 and divide by the total count.
Average Absolute Deviation = (21 + 2 + 12 + 13 + 5 + 17) / 6 = 70 / 6 ≈ 11.67
Therefore, the mean absolute deviation of the data set is approximately 11.67 to the nearest hundredth.