IM Alg1.1.12 Lesson: Standard Deviation
What do you notice? What do you wonder?
mean: 10, MAD: 1.56, standard deviation: 2 mean: 10, MAD: 2.22, standard deviation: 2.58 
mean: 10, MAD: 2.68, standard deviation: 2.92 mean: 10, MAD: 1.12, standard deviation: 1.61 
mean: 10, MAD: 2.06, standard deviation: 2.34 mean: 10, MAD: 0, standard deviation: 0 
Use the applet below to find the mean and the standard deviation for the data in the dot plots.
Partner 1
Dot plots: Partner 2
Dot plots: 
Conditions: Conditions:
What do you notice about the mean and standard deviation you and your partner found for the three dot plots?
Invent some data that fits the conditions. Be prepared to share your data set and reasoning for choice of values.
Begin with the data: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20
Use technology to find the mean, standard deviation, median, and interquartile range.
How do the standard deviation and mean change when you remove the greatest value from the data set?
How do they change if you add a value to the data set that is twice the greatest value?
What do you predict will happen to the standard deviation and mean when you remove the least value from the data set? Check to see if your prediction was correct.
What happens to the standard deviation and mean when you add a value to the data set equal to the mean?
Add a second value equal to the mean. What happens?
Add, change, and remove values from the data set to answer the question: What appears to change more easily, the standard deviation or the interquartile range? Explain your reasoning.
How is the standard deviation calculated? We have seen that the standard deviation behaves a lot like the mean absolute deviation and that is because the key idea behind both is the same.
Using the original data set, calculate the deviation of each point from the mean by subtracting the mean from each data point.
If we just tried to take a mean of those deviations what would we get?
There are two common ways to turn negative values into more useful positive values: take the absolute value or square the value. To find the MAD we find the absolute value of each deviation, then find the mean of those numbers. To find the standard deviation we square each of the deviations, then find the mean of those numbers. Then finally take the square root of that mean. Compute the MAD and the standard deviation of the original data set.