1. Some may be used more than once or not at all.
WARM – UP
Identify the A, B, and C position from each graph as the distribution’s Mean, Median, or Mode.
Some may be used more than once or not at all.
(a) (b) (c)
MEAN:
MEDIAN:
MODE: A B C C B A A

2. Warm - up
1. Find the Mean and Standard Deviation of:
8, 5, 6, 8, 18, 5, 11, 9, 8, 7, 9, 10

3. Draw a Box Plot from this Cumulative Histogram
Cumulative Curve

4. A B 0 1 2 3 4 5 6 7 8 9 10 1112 13 14 Length of Service (years)
Length of Service (years)
IQR = 4 years

5. CHAPTER 6

6. Example 1 – Effects of Changing Observations
1. Find the Mean and Standard Deviation of:
1, 8, 5, 4, 9, 3
2. Multiply each # by 2 AND then Add 6 find the new Mean and Standard Deviation. (What are the difference as compared to #1’s results?) 1. 2.

7. Adding and Subtracting each individual data value by a constant number will:
Increase/decrease the Center – Mean, Median,
and Mode.
NOT Change the Spread – Std Dev., IQR, Range.
Multiplying each individual data value by a scalar number will:
Change both the Center and Spread.

8. 1. How many tails would you expect to obtain?
If an experiment of Tossing a coin 20 times was performed with the variable of interest being the number of tails you obtain from 20 tosses,:
1. How many tails would you expect to obtain?
2. What kind of Distribution would you expect?
DENSITY CURVES
Density Curves are the smooth curves that represent the overall pattern of a Histogram or distribution. The AREA under the density curve represent the proportion of observations that fall in each range of values Entire curve = 100%
Uniform Distribution
Example:
HEADS TAILS

9. THE NORMAL CURVE

10. Notation (Symbols): Sample Population
Mean:
Standard Dev.:
Density Curves that are symmetric, single-peaked, and bell shaped are called Normal Distributions

11. Represents a Normal Distribution with Mean μ and Standard Deviation σ.
Z-Score – The value that indicates how many Standard Deviations an observation is from the Mean.
This is done with the z-score formula:

12. A student scores a 74% on Test #1
A student scores a 74% on Test #1. Test #1 has a mean (µ) equal to 86% and a Standard Deviation (σ) equal to 4.5%. How unusual is this student’s test score? (ie. How many standard deviation is the student’s score from the mean?)

13. HW: Page 123: 2-12 even (Omit #8)
French
Math

14. HW: Page 123: 2-12 even, 8

16. HW: Page 123: 2-12 even
a) standard deviations BELOW the mean.
b) 10 mph is more unusual.

17. a) Mean =3.84 Standard deviation = 3.56
b) Mean = Standard deviation = 5.73

19. National gas prices are at $2. 72 a gallon with Std. Dev. at $0. 09
National gas prices are at $2.72 a gallon with Std. Dev. at $ How unusual would it be to find a gas station charging $2.60 a gallon?
We must Standardize the Curve. This means that we are going to change the units so that the Mean = 0 and the Standard Deviation = This is done with a z-score.

20. Andy scored a 650 on the Math portion of the SAT
Andy scored a 650 on the Math portion of the SAT. Mary scored a 25 on the ACT. If the Math SAT has a Normal Distribution, , and the ACT has a Normal Distribution , which student did better and why?
ACT
SAT
Andy = (650 – 500 )/95 = 1.58
Mary = (25 – 21)/3 = 1.33

21. 4 Complete Response
All three parts essentially correct
3 Substantial Response
Two parts essentially correct and one part partially correct
2 Developing Response
Two parts essentially correct and one part incorrect OR
One part essentially correct and one or two parts partially correct
Three parts partially correct
1 Minimal Response
One part essentially correct and two parts incorrect
Two parts partially correct and one part incorrect

22. Characteristics of Density Curves:
1. It is always on or above the horizontal axis.
2. The area underneath the curve is always equal to ONE or (100%).
THE NORMAL CURVE

23. Characteristics of Density Curves
1. The area underneath the curve is always equal to ONE or (100%).
THE NORMAL CURVE