What is the mean absolute deviation (MAD) for the following set of data? (2, 5, 7, 1, 2)
A. 3.4
B. 2
C.2.08
D. 5
When put together, we can define mean deviation as the mean distance of each observation from the mean of the data. Mean Absolute Deviation Formula. Ratio of sum of all absolute values of deviation from central measure to the total number of observations. M.A. D = (Σ Absolute Values of Deviation from Central Measure) / (Total Number of Observations)
To calculate the mean absolute deviation (MAD) for a set of data, you need to follow these steps:
1. Find the mean (average) of the data set.
2. Subtract the mean from each data value to find the deviation.
3. Take the absolute value of each deviation.
4. Find the mean (average) of the absolute deviations.
Let's calculate the MAD for the given set of data step by step:
Step 1: Find the mean:
Mean = (2 + 5 + 7 + 1 + 2) / 5 = 17 / 5 = 3.4
Step 2: Find the deviations from the mean:
2 - 3.4 = -1.4
5 - 3.4 = 1.6
7 - 3.4 = 3.6
1 - 3.4 = -2.4
2 - 3.4 = -1.4
Step 3: Find the absolute deviations:
|-1.4| = 1.4
|1.6| = 1.6
|3.6| = 3.6
|-2.4| = 2.4
|-1.4| = 1.4
Step 4: Find the mean of the absolute deviations:
Mean of absolute deviations = (1.4 + 1.6 + 3.6 + 2.4 + 1.4) / 5 = 10.4 / 5 = 2.08
Therefore, the mean absolute deviation (MAD) for the given set of data is 2.08.
The correct option is C. 2.08.
To find the mean absolute deviation (MAD) for a set of data, you need to follow these steps:
1. Calculate the mean of the data set by adding up all the values and dividing by the total number of values.
For this data set (2, 5, 7, 1, 2), the mean is (2 + 5 + 7 + 1 + 2) / 5 = 3.4.
2. Calculate the absolute deviation for each value by subtracting the mean from each value and taking the absolute value of the result.
The absolute deviations for the data set are:
|2 - 3.4| = 1.4
|5 - 3.4| = 1.6
|7 - 3.4| = 3.6
|1 - 3.4| = 2.4
|2 - 3.4| = 1.4
3. Calculate the average of the absolute deviations by adding up all the absolute deviations and dividing by the total number of values.
The average of the absolute deviations for this data set is (1.4 + 1.6 + 3.6 + 2.4 + 1.4) / 5 = 1.88.
Therefore, the mean absolute deviation (MAD) for the given data set is approximately 1.88. None of the provided answer choices (A. 3.4, B. 2, C. 2.08, D. 5) match this result.