What is the mean absolute deviation for the data set 5, 6, 10

The Correct Answer and Explanation is :

Data Set: 5, 6, 10

To calculate the Mean Absolute Deviation (MAD), follow these steps:

Step 1: Find the mean (average) of the data set.

The formula for the mean is:

[
\text{Mean} = \frac{\sum x_i}{n}
]

Where:

( \sum x_i ) is the sum of all the data points.
( n ) is the number of data points.

For the data set ( 5, 6, 10 ):

[
\text{Mean} = \frac{5 + 6 + 10}{3} = \frac{21}{3} = 7
]

So, the mean is 7.

Step 2: Find the absolute deviations from the mean.

The absolute deviation for each data point is the absolute value of the difference between the data point and the mean.

[
|x_i – \text{Mean}|
]

For 5: ( |5 – 7| = 2 )
For 6: ( |6 – 7| = 1 )
For 10: ( |10 – 7| = 3 )

Step 3: Find the mean of the absolute deviations.

Now, we calculate the mean of these absolute deviations:

[
\text{MAD} = \frac{\sum |x_i – \text{Mean}|}{n}
]

Sum of the absolute deviations:

[
2 + 1 + 3 = 6
]

Now, divide by the number of data points ( n = 3 ):

[
\text{MAD} = \frac{6}{3} = 2
]

Final Answer:

The Mean Absolute Deviation (MAD) of the data set ( 5, 6, 10 ) is 2.

Explanation:

The Mean Absolute Deviation (MAD) is a measure of the spread or dispersion of a data set. It tells you, on average, how far each data point in the set is from the mean. Unlike the variance or standard deviation, which square the differences from the mean (making them larger), the MAD uses the absolute value of those differences, making it a simpler and more direct way of understanding how spread out the data points are. In this example, each data point deviates from the mean (7) by 2, 1, and 3 units, respectively. The MAD helps quantify this average deviation.