Statistics: Frequency Distributions & Graphs
Definitions
Raw Data
Data collected in original form.
Frequency
The number of times a certain value or class of values occurs.
Frequency Distribution
The organization of raw data in table form with classes and
Stats: Estimating the Mean
You are estimating the population mean, mu, not the sample mean, x bar.
Population Standard Deviation Known
If the population standard deviation, sigma is known, then the mean has a normal (Z)
distribution.
The maximum error of
Stats: F-Test
Definitions
F-distribution
The ratio of two independent chi-square variables divided by their respective
degrees of freedom. If the population variances are equal, this simplifies to be
the ratio of the sample variances.
Analysis of Variance
Stats: Estimation
Definitions
Confidence Interval
An interval estimate with a specific level of confidence
Confidence Level
The percent of the time the true mean will lie in the interval estimate given.
Consistent Estimator
An estimator which gets closer
Stats: Estimating the Proportion
You are estimating the population proportion, p.
All estimation done here is based on the fact that the normal can be used to
approximate the binomial distribution when np and nq are both at least 5. Thus, the p
that were
Stats: Counting Techniques
Definitions
Factorial
A positive integer factorial is the product of each natural number up to and
including the integer.
Permutation
An arrangement of objects in a specific order.
Combination
A selection of objects without rega
Stats: Normal Distribution
Definitions
Central Limit Theorem
Theorem which stats as the sample size increases, the sampling distribution of
the sample means will become approximately normally distributed.
Correction for Continuity
A correction applied to
Stats: Probability
Definitions
Probability Experiment
Process which leads to well-defined results call outcomes
Outcome
The result of a single trial of a probability experiment
Sample Space
Set of all possible outcomes of a probability experiment
Event
On
Stats: Hypothesis Test: Pi = 3.2?
In 1897, legislature was introduced in Indiana which would make 3.2 the official
value of pi for the State. Now, that sounds ridiculous, but is it really?
Claim: Pi is 3.2.
To test the claim, we're going to generate a who
Stats: Correlation
Sum of Squares
We introduced a notation earlier in the course called the sum of squares. This notation
was the SS notation, and will make these formulas much easier to work with.
Notice these are all the same pattern,
SS(x) could be wri
Stats: Conditional Probability
Conditional Probability
Recall that the probability of an event occurring given that another event has already
occurred is called a conditional probability.
The probability that event B occurs, given that event A has already
Stats: Binomial Probabilities
Binomial Experiment
A binomial experiment is an experiment which satisfies these four conditions
A fixed number of trials
Each trial is independent of the others
There are only two outcomes
The probability of each outcome rem
Statistics: Data Description
Definitions
Statistic
Characteristic or measure obtained from a sample
Parameter
Characteristic or measure obtained from a population
Mean
Sum of all the values divided by the number of values. This can either be a
population
Statistics: Grouped Frequency Distributions
Guidelines for classes
1.
There should be between 5 and 20 classes.
2.
The class width should be an odd number. This will guarantee that the class
midpoints are integers instead of decimals.
3.
The classes must
Statistics: Introduction
Population vs Sample
The population includes all objects of interest whereas the sample is only a portion of
the population. Parameters are associated with populations and statistics with samples.
Parameters are usually denoted us
Stats: Correlation & Regression
Definitions
Coefficient of Determination
The percent of the variation that can be explained by the regression equation
Correlation
A method used to determine if a relationship between variables exists
Correlation Coefficien
Stats: Chi-Square
Definitions
Chi-square distribution
A distribution obtained from the multiplying the ratio of sample variance to
population variance by the degrees of freedom when random samples are
selected from a normally distributed population
Contin
Stats: Coefficient of Determination
Coefficient of Determination
The coefficient of determination is .
the percent of the variation that can be explained by the regression equation.
the explained variation divided by the total variation
the square of r
Wh
Stats: Central Limit Theorem
Sampling Distribution of the Sample Means
Instead of working with individual scores, statisticians often work with means. What
happens is that several samples are taken, the mean is computed for each sample, and
then the means
Stats: Probability Rules
"OR" or Unions
Mutually Exclusive Events
Two events are mutually exclusive if they cannot occur at the same time. Another
word that means mutually exclusive is disjoint.
If two events are disjoint, then the probability of them bot
Stats: Measures of Position
Standard Scores (z-scores)
The standard score is obtained by subtracting the mean and dividing the difference by
the standard deviation. The symbol is z, which is why it's also called a z-score.
The mean of the standard scores
Stats: One-Way ANOVA
A One-Way Analysis of Variance is a way to test the equality of three or more means
at one time by using variances.
Assumptions
The populations from which the samples were obtained must be normally or
approximately normally distribute
Stats: Hypothesis Testing
Definitions
Null Hypothesis ( H0 )
Statement of zero or no change. If the original claim includes equality (<=, =, or
>=), it is the null hypothesis. If the original claim does not include equality (<, not
equal, >) then the null
Stats: Measures of Variation
Range
The range is the simplest measure of variation to find. It is simply the highest value
minus the lowest value.
RANGE = MAXIMUM - MINIMUM
Since the range only uses the largest and smallest values, it is greatly affected b
TI-82: Generating Random Numbers
You can generate random numbers on the TI-82 calculator using the following
sequence. N is the number of different values which could be and S is the
minimum number.
int (N*rand+S)
INT is found under the MATH menu (math nu
Stats: Two-Way ANOVA
The two-way analysis of variance is an extension to the one-way analysis of variance.
There are two independent variables (hence the name two-way).
Assumptions
The populations from which the samples were obtained must be normally or
a
TI-82: Lists and Statistics
There are two features of the TI-82 calculator that will be used. Lists and
Statistics. The STAT key is located at the top center of the calculator and the
LIST key is obtained by 2nd STAT.
There are six lists that you can work
TI-82: Plotting an Ogive
The Ogive is a frequency polygon (line plot) graph of the cumulative frequency
or the relative cumulative frequency.
The horizontal axis is marked with the class boundaries and the vertical axis is
the frequency. All class boundar
Stats: Measures of Central Tendency
The term "Average" is vague
Average could mean one of four things. The arithmetic mean, the median, midrange,
or mode. For this reason, it is better to specify which average you're talking about.
Mean
This is what peopl
Stats: Test for Independence
In the test for independence, the claim is that the row and column variables are
independent of each other. This is the null hypothesis.
The multiplication rule said that if two events were independent, then the probability
of