1. Daily Warm-up Tuesday, April 29th
What type of bond holds water molecules together? What about the hydrogen and oxygen in a water molecule? Which one is stronger? Why?

2. Terms Populations versus samples
Populations of organisms vary in characteristics
Weight, growth rate, size
Statistics enable summarization of characteristics
Takes a sample from the population
****MUST BE RANDOM****
All individuals have equal chance of being chosen
Larger the better
Enable us to determine whether two populations are statistically different

3. μ A parameter is a numeric quantity
usually unknown
describes a certain population characteristic
Ex. Mean and median
Represented by Greek letters μ
A statistic is a quantity, calculated from a sample of data, used to estimate a parameter
Ex. Mean

4. Mean
Most commonly used parameter to describe the central tendency of a population
Parameter: μ (true mean)
Statistic:

5. Median Think middle of the road Another measure of central tendency
Middle measurement in ranked listing
If there is even number of individuals in the sample, median is mean of the two middle measurements

6. When it might be better to use the median to describe the central tendency:
OUTLIERS!
11, 12, 13, 14, 15, 14, 16, 18, 13, 110

7. Variability How data falls around the mean Sample 1 Sample 2 9 15 229 15 22 16 17 13 11 19 14
Mean = 15

8. Histograms are a good way of displaying variability

9. Range is one measure of data variability
Difference between the largest and the smallest measurement
Ex. Range (9, 22) for Sample 1
Range gives us a good “eyeball” estimate for variability BUT:
Range almost always underestimates actual population range

10. Sum of Squares
More accurate method of estimating variation from the mean is the standard deviation
Sum of Squares
SS = Σ(X – )2

11. Sum of Squares example SS = Σ(X – )2
Sample 1 9
(9-15)2 22
(22-15)2 16
(16-15)2 13
(13-15)2 11
(11-15)2 19
(19-15)2
Mean = 15
122
***Why is it important that we square the values?

12. Try it with sample 2
What is the sum of squares value?

13. SS= 10

14. Variance (s2)
Value from SS can be used to calculate the sample variance
s2 = SS/DF
DF= Degrees of freedom (n-1)
n is the number of samples
Ex. Sample 1 has n=6, n-1=5
***DF will be n-1

15. What is variance for Sample 2?

16. s2 =2

17. Standard Deviation (s)
Report the standard deviation, rather than the sample variance
***Shows us the variability in samples***
s or SD =

18. What is SD or s of sample 2?

19. s= 1.41

20. Why is this important? STDEV and relationship with mean
Histogram on board
Sample 2 had s= 1.41
Sample 1 had s= 4.94
SS=122
s2 = 122/5= 24.4
Square root of 24.4= 4.94