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DSST Principles of Statistics
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Terms in this set (29)
Data Types - Numerical Data
Data that can be counted or measured.
Examples: number of fish in a net, speed of sound, etc
Data Types - Numerical - Discrete Data
Represents units that can be counted. The range can be infinite or limited. But there must be countable units
Examples: number of times a particular coin can be flipped before it shows heads, how many steps it takes a person to walk 1 mile.
Data Types - Numerical - Continuous Data
Can be absolutely any value in a range but not directly countable.
Examples: weight of a wedge of cheese cut from a 10lb wheel (anything less that 10lb, but impossible to count a the possibilities)
Data Types - Categorical Data
Not counted or measured as a number. It represents info that can be divided into categories.
Examples: zip codes, favorite foods,
Data Types - Categorical - Ordinal
Categorical data that has been organized into meaningful numbers.
Examples: survey of likelihood to vote on scale 1-5 - can analyze the numbers that represent something
Levels of Measurement
Levels that describe exactly how variables in a study are measured.
4 Levels - nominal, ordinal, interval, and ratio
Level of Measurement - Nominal
Categories that are not ranked or related.
Example: types of cars
Level of Measurement - Ordinal
Places data into ranked categories (ie in relative order to one another). Use of terms 1st, 2nd, 3rd... are good clues that ordinal
Example: finishing place of each runner in a race.
Level of Measurement - Interval
Places a set distance between categories of data.
Example: there is the same distance between a size 2 & size 3 shirt as between a size 15 & 16.
Note: 0 does not mean nothing in this method!
Level of Measurement - Ratio
At this level, 0 actually means zero!
Example: counting the number of trees - 0 trees means no trees.
Sampling Methods
Methods of collecting the data to analyze.
Methods:
-Probability
-Simple random
-Stratified random
-Multistage
Population
All members of the group under consideration.
Sample
The portion of the population chosen to analyze.
Sample Design
Refers to the method used to choose a sample.
Key - making sure the sample is truly representative of the entire population.
Voluntary Response Sample
An example of poor design.
The entire population is surveyed, but data is only collected from those who choose to complete the survey.
"Biased"
A sample that is not reflective of the population.
Avoid by choosing some impersonal, impartial means.
Sample Method - Probability Sample
The best method. (several types)
Each member of a population has a known, positive chance of being chosen.
Sample Method - Simple Random Sample (SRS)
In the study population, every subset of 'n' individuals has the same probability of being chosen. Note: this means any group of 10 individuals has the same chance of being chosen as any other group of 10.
Sample Method - Stratified Random Sample
More complicated, but more powerful.
Population categorized into groups of similar individuals called strata, then a random sample is chosen from within each stratum.
Often smaller & easier to carry out; usually as good as or better then SRS.
Sample Method - Multistage Sampling
Useful in narrowing down a sample from a large diverse population.
Increasingly smaller samples are chosen. Each sample may be SRS or stratified. Used by US Census Bureau & major pollsters.
Undercoverage
Data collection pitfall.
Refers to when some groups are left out or underrepresented in a sample.
Nonresponse
A data collection problem that occurs when individuals chosen as part of a sample don't participate - whether by accident or because of lack of cooperation.
Response Bias
Respondents not answer accurately.
Makes it of vital importance to be careful how word survey questions.
Descriptive Statistics
Provide basic summary info of a data set, particularly its distribution.
Distribution (of a data set)
The pattern of variation within it, often summarized with a few key values.
Range (of a data set)
The complete spread of values in a distribution.
Center of a Distribution (of data set)
Refers to the values near the middle of the range
Most common measure: mean
Spread of distribution (of data set)
Describes how far the values in the distribution spread out from the center
Mean
The average. Symbol: /x (when the data under consideration is a sample) or grk symbol - looks like a mix of p & u (full population being considered).
/x = (X1+X2+X3+...+Xn)/n = (1/n)[sum]Xi
Not a RESISTANT measure of the center - susceptible to outliers.
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Verified questions
PROBABILITY
A card is chosen from a pack of cards. Are the events that a card from one of the two red suits is chosen and that a card from one of the two black suits is chosen mutually exclusive? What about the events that an ace is chosen and that a heart is chosen?
PROBABILITY
At Thomas Jefferson High School, the student body is divided by age as follows: 7% of the students are 14,22% of the students are 15,24% of the students are 16,23% of the students are 17,19% of the students are 18, and the rest of the students are 19, Find the average age of the students at Thomas Jefferson High School.
STATISTICS
Some schools teach reading using phonics (the sounds made by letters) and others using whole language (word recognition). Suppose a school district wants to know which method works better. Suggest a design for an appropriate experiment.
PROBABILITY
Suppose a certain type of small data processing firm is so specialized that some have difficulty making a profit in their first year of operation. The probability density function that characterizes the proportion Y that make a profit is given by $$ f(y)=ky^4(1-y)^3, \text{ for } 0 \leq y \leq 1, $$ $$ f(y)=0, \text{ elsewhere.} $$ (a) What is the value of k that renders the above a valid density function? (b) Find the probability that at most 50 % of the firms make a profit in the first year. (c) Find the probability that at least 80% of the firms make a profit in the first year.