Question

Please help! This is worth a 100 points!

Answer 1

• 
  `MAD = 3.2`

Task :

• To evaluate the mean absolute deviation of the given data.

Solution :

In order to find the mean absolute data , firstly we need to find out the mean of the given data.

• Mean = (Sum of all observations)/(Total number of observations)
• Mean = [3 + 5 + (-1) + (-2) + (-5)]/[5]
• Mean = 0/5
• Mean = 0

Thus, mean = 0

Now,

We will find out the absolute difference for each data point given by subtracting the mean from each of them and taking the absolute value,

• |3-0| = 3
• |5-0| = 5
• |-1-0| = 1
• |-2-0| = 2
• |-5-0| = 5

Now ,

we'll calculate the average of the above absolute differences which would be the required absolute deviation.

• (3+5+1+2+5)/5 = 16/5 = 3.2

Thus, the mean absolute deviation (MAD) for the given data would be equal to 3.2.

Answer 2

3.2

Explanation:

Given data set:

• 3, 5, -1, -2, -5

The mean absolute deviation (MAD) measures the average distance between each data point and the mean of the data set.

To find the mean absolute deviation (MAD), first calculate the mean of the data set.

`\begin{aligned}\textsf{Mean of the data set}&=\frac{\textsf{Sum of all data points}}{\textsf{Total number of data points}}\\\\&=(3+5+(-1)+(-2)+(-5))/(5)\\\\&=(0)/(5)\\\\&=0\end{aligned}`

Find the absolute deviation of each data point from the mean by subtracting the mean from each data point and taking the absolute value:

`|3-0|=3`

`|5-0|=5`

`|-1-0|=1`

`|-2-0|=2`

`|-5-0|=5`

Calculate the mean of these absolute deviations:

`\begin{aligned}\textsf{Mean of the absolute deviations}&=\frac{\textsf{Sum of all absolute deviations}}{\textsf{Total number of data points}}\\\\&=(3+5+1+2+5)/(5)\\\\&=(16)/(5)\\\\&=3.2\end{aligned}`

Therefore, the mean absolute deviation (MAD) for the given data set is 3.2.