1. A class took a quiz. The class was divided into teams of 10
A class took a quiz. The class was divided into teams of 10. and each class had a mean 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?

2. Class A
Mean
Class B

3. NO
The mean does not tell us anything about the grade distribution or variation of grades in the population
Need a way to measure
the spread of grades

4. Mean and range tell only part of the ‘story’
Mean average
Mean and range tell only part of the ‘story’
Range (spread)
Here, most of the numbers hover around the mean, and are not evenly distributed throughout the range.

5. =
mean
-9.5
Standard Deviation is a measure of how spread out the values in the data set are from the mean

6. SD is useful for making comparisons between data sets beyond visual impressions
looks like a difference, but is it?
In biology, to describe a population
In education to calculate a grade curve
In production systems as the upper and lower control limit; anything above or below represents a problem.
In finance, the higher the standard deviation, the riskier the investment
For sports teams, a high standard deviation shows that they perform well in some situations but not in others.
Regarding climate while two cities may each have the same average maximum temperature, the standard deviation of the daily maximum temperature for a coastal city will be less than that of an inland city

7. SD describes a population
If SD is small , the data is closer to the mean. More likely the IV is affecting the DV If SD is LARGE, the numbers are spread out from the mean. Other factors likely influencing the DV
In biology, to describe a population
In education to calculate a grade curve
In production systems as the upper and lower control limit; anything above or below represents a problem.
In finance, the higher the standard deviation, the riskier the investment
For sports teams, a high standard deviation shows that they perform well in some situations but not in others.
Regarding climate while two cities may each have the same average maximum temperature, the standard deviation of the daily maximum temperature for a coastal city will be less than that of an inland city
SD describes a population

8. The Normal (Bell) curve
F D C B A
mean
+/- 1 standard deviation = 68.3% of the group
+/- 2 SD = 95.4% of the group

9. SD = the difference of all of the values from the mean of the population, summed, divided by the population size
N-1? The standard deviation of a sample of a population uses 1/(N-1), generating an unbiased estimate.
In the rare case when an entire population is counted/measured, the standard deviation calculation uses 1/N. ]

10. Here are the scores on the math quiz for team A:72 76 80 81 83 84 85 89
Here are the scores on the math quiz for team A:
ranked low to high
mean = 81.5

11. 1. Find all the distances from the mean (81.5)
Distance from 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
To find the standard deviation …
1. Find all the distances from the mean (81.5)

12. 2. Square each of the distances (to turn them into positive numbers)
score
d from Mean d2 72 76 80 81 83 84 85 89 =
- 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
2. Square each of the distances (to turn them into positive numbers)

13. 3. Add up all the squares Sum: 214.5 score d from Mean d2 72 76 80 8183 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
3. Add up all the squares

14. 4. Divide by (n - 1) where n represents the total amount of numbers
score
d from Mean d2
90.25
30.25
2.25
0.25
6.25
12.25
56.25 72 76 80 81 83 84 85 89
- 9.5
- 5.5
- 1.5
- 0.5
1.5
2.5
3.5
7.5
Sum:
214.5
(10-1)
= 23.8
4. Divide by (n - 1) where n represents the total amount of numbers

15. 5. Take the square root of the average distance
score
d from Mean d2
90.25
30.25
2.25
0.25
6.25
12.25
56.25 72 76 80 81 83 84 85 89
- 9.5
- 5.5
- 1.5
- 0.5
1.5
2.5
3.5
7.5
Sum:
214.5
______
10-1
= 23.8
the variance
SD = 4.88
5. Take the square root of the average distance
4.88 is the SD for this group

16. The standard deviation for Team B’s grades
d from Mean d2 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
variance
SD = 15.91
The standard deviation for Team B’s grades

17. Comparing the two classes
Team A
Team B
Average on the Quiz
Standard Deviation
On Team A, 68% of the scores (7 of 10) were between 77 and 86, compared to Team B where 68% of the students (7 of 10) scored between 65 and 97.
Verify by looking at the original distribution of each set of scores! (slide 2)

18. TEAM A TEAM B
81.5 +/ vs /

19. TRY IT YOURSELF:
A wildlife biologist measures the weight at birth of each of 5 pups in a litter of wolves. He finds the following:
gender birth weight in kg
M 2.2
M 2.8
F 1.8
F 2.4
F 2.5
Find the mean, variance, and standard deviation of the litter