Mean Absolute Deviation and Standard Deviation

MAD vs. Standard Deviation Lesson

This lesson is going to walk you through an activity comparing how MAD and Standard Deviation are calculated.

MAD vs. Standard Deviations

• These two statistical measures are used to described how data points are spread out from the mean.

• So to begin this activity calculate the mean of the data values in the table to the right

Multiple Choice

What was the mean of the data values?

• 217.75

• 75

• 250

• 187

How is MAD calculated?

• To begin Calculating the mean absolute deviation, we need to find the distance between each data value and the mean.

• I left the first and last lines of the table as examples.

• On your own paper you need to fill in the rest of the values and find the sum of the absolute values.

Multiple Choice

The sum was....

• 220

• 250

• 360

Calculating MAD continued

• On the right you will see that to calculate MAD, we divide the sum of absolute values by the number of data points

• In the last slide we found that our sum was 220 and we have 8 data points

• Therefore the MAD is 220 divide by 8 which is......

Multiple Choice

The MAD from the last slide is

• 27.50

• 0.04

Standard Deviation

• To begin calculating the standard deviation we need to know the distance between each data point and the mean. Then we square them and add them up

• Take the first row for example

• 182-217.75 = -35.75

• -35.75 * -35.75 = 1278.0625

• Finish the table and find the sum of the last column

Multiple Choice

The sum was

• 6661.5

• 6001.5

• 789.56

Standard Deviation

• To finish calculating SD, we use this formula:  $\sqrt{\frac{sum}{number\ of\ data\ values\ -\ 1}}$  

• so  $\sqrt{\frac{6661.5}{7}}$  = 30.85

• 
  

In geometry

• We will only be looking at Standard Deviation

• and don't worry about all the calculating :) I am going to show how to use technology in the next video in Schoology