Probability and Statistics
Study Help for Final Exam
Unit 1 – Terms and Graphs
1)
(a) Parameter – Value from a Population
Mean
Variance
Standard Deviation
Proportion

2
Mean
Variance
Standard Deviation
Proportion

p
2)
2 Branches of Statistics:
(a)
Descriptive – describes the situation
(b)
Inferential – makes predictions
3)
2 Types of Variables:
(a)
Quantitative – Numerical
4)
(b) Statistic – Value from a Sample
(b)
x
s
s2
p̂
Qualitative – Categorical
4 Types of Variables:
(a)
Nominal – Categories with NO order or ranking
(b)
Ordinal – Categories WITH order or ranking
(c)
Discrete – Can Count
Quantitative
(d)
Continuous – Can Measure
Qualitative
5)
5 Sampling Methods:
(a)
Convenience – easy access
(b)
Random – Every member has equal chance of selection
(c)
Systematic – Every “kth”
(d)
Stratified – A few from all
Grouped
(e)
Cluster – All from a few
6)
Graphs:
(a)
Circle Graph – Shows parts to a whole
(b)
Bar Graph – Bars don’t have to touch; Proportional Rectangular Area for frequency.
(c)
Pareto Chart – A bar graph in descending order.
(d)
Dot Plot – Dots above a horizontal line; Dots represent frequency
(e)
Stem and Leaf – Stems can be more than one number; leaves are a single number
(f)
Time Series – a line graph that shows progress over time.
(g)
Histogram – Bars Touch; For Quantitative Data
7)
Circle Graph: Data is in a frequency table.
Area
8)
Bar Graph:
# Vacationing
% = f/n x 100
Degree = f/n x 360
Great Lakes
37
37
x100  7.4
500
37
x360  27 
500
New England
104
20.8
75
East Coast
206
41.2
148
South
96
19.2
69
West Coast
57
11.4
41
n = 500
100%
360 degrees
Soft Drink
Number
Favorite Soft Drinks
30
18
Coke
25
Root Beer
10
Dr. Pepper
12
Orange
7
25
Frequency
Sprite
20
15
Series1
10
5
0
Sprite
9)
Pareto Chart:
Frequency
Crimes in New York City
Series1
Assault
Rape
Robbery
Root Beer Dr. Pepper
Stem and Leaf:
Stem
Leaf
0
2
1
3
4
2
0
3
5
3
1
2
2
2
4
3
4
4
5
5
1
2
7
Homicide
Type
Key:
11)
Dot Plot:
12)
Stem
Leaf
0
2
1
3
4
2
0
3
5
3
1
2
2
2
4
3
4
4
5
5
1
2
7
Key:
1/3 = 13
2
3
6
Orange
Type
10)
180
160
140
120
100
80
60
40
20
0
Coke
Time Series:
1/3 = 13
2
3
6
13)
Histograms: Drawn from a frequency distribution.
Normal
Right or Positive Skew
Left or Negative Skew
Bimodal
Uniform
Unit 2 – Center and Variation
Measures of Center
Mean
Median
Mode
Midrange
Measures of Variation
Range
Standard Deviation
Variance
Use your graphing calculator to find mean, standard deviation, variance.
Arrays
a)
b)
Numbers that are not in a frequency distribution table. Ex:
Put numbers in L1.
Can find using one of 2 calculator methods:
Method 1
Stat
Calc
One Variable Stats
L1, L2
Enter
Method 2
Go to Home Screen
2nd Stat
Math
Operation Needed. Ex: mean(L1, L2)
Enter
Ungrouped Data
Grouped Data
a)
Single digit numbers in L1 and frequencies in L2. Ex:
Intervals of numbers in class and frequencies in L2. Ex:
Find the midpoints of each interval and put them in L1. Midpoint =
Low 
High 
2
.
Put frequencies in L2. Then use the same set of instructions as Ungrouped Data above.
Unit 3 – Measures of Position
Measures of Position:
a) Quartiles
b) Percentiles
c) z-scores
d) Box Plots
Percentiles: A set is divided into 100 equal parts.
Use C 
np
to locate a number at a percentile.
100
Percentiles
Quartile Equivalent
P25
Q1
P50
Q2 or Median
P75
Q3
Examples:
1) Find P75 of the data set
2) Find P60 of same data set.
Z-Scores:
z  score 
z
Box Plots and Outliers:
(value  mean)
st .deviation
x  x 
s
or z 
x   

Unit 4 – Correlation and Regression
4 Types of Correlation:
Correlation Coefficient – “r” – Measures the Strength:
Regression – Finds the equation of the Line of Best Fit. Used to make predictions.
Unit 5 – Counting Rules
Sample Space – All possible outcomes for a chance experiment.
a)
d)
Tree Diagrams
Multiplication Rule
Permutations – Order Matter
Combinations – Order Does NOT Matter
b) Lists
c) 2-Way Tables
e) Permutations and Combinations
Unit 6 – Probability
Unit 7 – Probability Distributions
You may use the formulas above; however, there is a recommended shortcut using GDC:
Mean = 1.9
St. Deviation = 1.14
L1
L2
Unit 8 – Expectation and Binomial
Expectation:
Binomial Probability:
Variance = (1.135781669)²=1.29
Binomial Probability with more than 1 “x”:
x= 0, 1, 2, 3
x= 3, 4,….20
Mean, St. Dev. And Variance of a Binomial:
Mean :   np
Variance :  2  npq
St.Deviation :   npq
Unit 9 – Normal Distributions
Empirical Rule:
Standard Normal Distributions:
Mean = 0 and St. Deviation = 1
To find Area: ncdf (z , z)
To find z-score: InvNorm(Area Left)
Normal Distributions: Mean is NOT zero. Must convert to Standard Normal by using a z-score in
order to use GDC.
Finding Area/Probability:
z
x

Finding Cutoff Scores (“X” Values):
Unit 10: Sampling Distributions
Treat Sampling Distributions the same as Normal Distributions EXCEPT FOR ONE THING:
The standard deviation of a normally distributed set with a sample size given is the following:
Notice that the standard deviation is
now different!
Unit 11 – Confidence Intervals
Sample Size Formulas:
Proportion
 z
n  pˆ qˆ  2
 E





Mean
2
Always round decimal answers UP.
 z 
n 2
 E





2
Always round decimal answers UP.
To Find Actual Intervals use GDC rather than the formulas:
Finding Intervals on Calculator:
1) Stat
2) Tests
3) GDC:
Z Interval
T Interval
Proportion Interval
Unit 12 – 1 Sample Hypothesis Tests
Traditional Method:
1.
2.
3.
4.
5.
Set Up Ho, Ha, and Claim. Draw Sketch
Find CV(s)
Find Test Values
State Conclusion – Reject Ho/Fail to Reject Ho
State Result – Support Claim/Do Not Support Claim
7: ZInterval
8: TInterval
A: 1-PropZInt