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