1. Do-Now-Day 2 Section 2.2
Find the mean, median, mode, and IQR from the following set of data values:
60, 64, 69, 73, 76, 122
Mean-
Median-
Mode-
InterQuartile Range-
What does the value of 122 do to the data set?
Is it an outlier?

3. Standard Deviation Chapter 2-Section 2
Standard Deviation Chapter 2-Section 2.2 What does the standard deviation show?

4. Two classes took a recent quiz
Two classes took a recent quiz. There were 10 students in each class, and each class had an average score of Since the averages are the same, can we assume that the students in both classes all did pretty much the same on the exam?

5. The answer is… No. The average (mean) does not tell us anything about the distribution or variation in the grades. What type of graph would show the distribution?

6. Dot Plots!!! Here are Dot-Plots of the grades in each class:

7. Mean
Which
Scores
Are close
To the
Average?

8. So, we need to come up with some way of measuring not just the average, but also the spread of the distribution of our data.

9. The Standard Deviation is a number that measures how far away each number in a set of data is from their mean. It is always positive! It takes in account ALL the numbers in the data set. Not like Median, mode, etc You can use the standard deviation to compare the spread of two data sets.

10. If the Standard Deviation is large, it means the numbers are spread out from their mean. If the Standard Deviation is small, it means the numbers are close to their mean.

11. Here are the scores on the math quiz for Team A:72 76 80 81 83 84 85 89
Average:
81.5
Are the scores “close” to the average? Let’s See…

12. Now, lets compare the two classes What can you say about both classes?
Average on the Quiz
Standard Deviation

13. The Standard Deviation measures how far away each number in a set of data is from their mean.
For example, start with the lowest score, 72. How far away is 72 from the mean of 81.5?
= - 9.5
- 9.5

14. Or, start with the lowest score, 89
Or, start with the lowest score, 89. How far away is 89 from the mean of 81.5?
= 7.5
- 9.5
7.5

15. Notes How to Find Standard Deviation Find all distance away from mean
2. Square the distances to make them positive
3. Add up all the distances
4. Divide by (n-1),
where n represents the amount of numbers
This is the variance
5. Take the square root of that number

16. Distance from Mean
So, the first step to finding the Standard Deviation is to find all the distances from the mean. Always best to make a table! 72 76 80 81 83 84 85 89
-9.5
7.5

17. Distance from Mean
So, the first step to finding the Standard Deviation is to find all the distances from the mean. 72 76 80 81 83 84 85 89
- 9.5
- 5.5
- 1.5
- 0.5
1.5
2.5
3.5
7.5

18. Distance from Mean
Distances Squared
Next, you need to square each of the distances to turn them all into positive numbers 72 76 80 81 83 84 85 89
- 9.5
- 5.5
- 1.5
- 0.5
1.5
2.5
3.5
7.5
90.25
30.25

19. Distance from Mean
Distances Squared
Next, you need to square each of the distances to turn them all into positive numbers 72 76 80 81 83 84 85 89
- 9.5
- 5.5
- 1.5
- 0.5
1.5
2.5
3.5
7.5
90.25
30.25
2.25
0.25
6.25
12.25
56.25

20. Add up all of the distances
Distance from Mean
Distances Squared
Add up all of the distances 72 76 80 81 83 84 85 89
- 9.5
- 5.5
- 1.5
- 0.5
1.5
2.5
3.5
7.5
90.25
30.25
2.25
0.25
6.25
12.25
56.25
Sum:
214.5

21. Divide by (n - 1) where n represents the amount of numbers you have.
Distance from Mean
Distances Squared
Divide by (n - 1) where n represents the amount of numbers you have. 72 76 80 81 83 84 85 89
- 9.5
- 5.5
- 1.5
- 0.5
1.5
2.5
3.5
7.5
90.25
30.25
2.25
0.25
6.25
12.25
56.25
Sum:
214.5
(10 - 1)
= 23.8

22. Finally, take the Square Root of the average distance
Distance from Mean
Distances Squared
Finally, take the Square Root of the average distance 72 76 80 81 83 84 85 89
- 9.5
- 5.5
- 1.5
- 0.5
1.5
2.5
3.5
7.5
90.25
30.25
2.25
0.25
6.25
12.25
56.25
Sum:
214.5
(10 - 1)
= 23.8
= 4.88

23. This is the Standard Deviation- which means
Distance from Mean
Distances Squared
This is the Standard Deviation- which means 72 76 80 81 83 84 85 89
- 9.5
- 5.5
- 1.5
- 0.5
1.5
2.5
3.5
7.5
90.25
30.25
2.25
0.25
6.25
12.25
56.25
Sum:
214.5
(10 - 1)
= 23.8
= 4.88

24. Now find the Standard Deviation for the other class grades
Distance from Mean
Distances Squared
Now find the Standard Deviation for the other class grades 57 65 83 94 95 96 98 93 71 63
- 24.5
- 16.5
1.5
12.5
13.5
14.5
16.5
11.5
- 10.5
-18.5
600.25
272.25
2.25
156.25
182.25
210.25
132.25
110.25
342.25
Sum:
2280.5
(10 - 1)
= 253.4
= 15.91

25. Now, lets compare the two classes again What can you say about both classes?
Average on the Quiz
Standard Deviation

26. The good news is that the calculator can do this for us 
The bad news is that I would like you to practice one more by hand 
Good and Bad News

27. How to find standard deviation on the calculator
Practice Problem #1: Calculate the standard deviation.
Test Scores: 22, 99, 102, 33, 57, 75, 100, 81, 62, 29
How to find standard deviation on the calculator

28. How to find the standard deviation using a calculator
Put data in L1
STAT---EDIT---Enter Data into a List (L1)
2. Press STAT ->Calc 1-VarStats (L1)
3. 2nd 1 (L1 ) ENTER
4. The standard deviation is sx value
Let’s try it with this data

29. When to Use Each Description
If your data is skewed:
Mean and standard deviation are strongly effected by outliers
Median and quartiles are less affected

30. When to Use Each Description
If your data is symmetric:
The mean and median are very close in value
Both IQR and standard deviation are valid measures of spread
The mean and standard deviation should be used for symmetric distributions that are free of outliers.

31. Quick Question to think about
. The standard deviation should not be used to measure spread when
(a) the distribution is normal
(b) the mean is used to measure center
(c) the distribution is symmetric
(d) the distribution is skewed
(e) the data has been transformed

33. Example
Here is a dotplot showing the number of music CDs owned by students in a college statistics class.
What would better summarize the center and spread of the distribution the mean and standard deviation or the median and IQR?