BStats Exam 1

Descriptive Statistics

Use summary statistics, graphs, and tables to describe data sets

Inferential Statistics

Use samples to draw inferences about larger populations (some level of uncertainty)

• Hypothesis testing, confidence intervals, linear regression

Summary Statistics

Descriptive- measures of location, central tendency, spread of data

Data Visualization

Descriptive- histograms, scatterplots, pie charts

Probability

Likelihood of different outcomes of events occurring

• Ex: Risk assessment, inventory management, project management, investment analysis

Population

All individuals, objects, or measurements where properties are being studied

Sample

Subset of population being studied

Sampling

Process of choosing a subject to study

Statistic

Numerical characteristic of a sample; estimates corresponding population parameter

• Ex: Average

Parameter

Number used to represent population characteristics and generally cannot be determined easily. Concluding factor, end goal

Benefits of Sampling

• Reduced costs (More info to gather costs more)

• Greater speed (Gathering more info takes longer)

• Greater Scope (Fewer individuals allows more time with each one to gather info)

• Accuracy (Less time needed means more knowledgeable/trained people to gather it)

• Representative sample

Representative Sample

When the sample has the same characteristics as the population it represents

Simple Random Sampling

Use a random method to select a sample, needs info about the whole population

• Ex: Random number generator, random number table, drawing lots

Stratified Sampling

1. Divide population into groups called strata

2. Allocate sample size to each stratum so they’re proportional to the size in the population (ensures minority representation)

3. Use all or a simple random sample within the selected clusters

   • Don’t need a lot of info

Systematic Sampling

Randomly select starting point and pick only the nth individual

• Don’t need a lot of info

Convenience Sampling

Use a sample that is convenient

• Don’t need a lot of info

Common Sampling Issues

• Sampling bias

• Sample size issues

• Undue influence (Ethical issues)

• Self-selected samples (Opinionless people will not respond)

• Non-response bias (Certain demographics may not respond)

• Time bias (Holidays)

Qualitative Data (Categorical)

Result of describing attributes of a population/sample

• Ex: Customer reviews

Quantitative Data

Result of counting/measuring attributes of a population/sample

• Always a number

Discrete Quantitative Data

Only takes on certain numerical data

• Ex: # of customers per day

Continuous Quantitative Data

Can include fractions, decimals, and irrational numbers

• Ex: Lengths of wood boards

Levels of Measurement

Way a set of data is measured

Nominal Scale

Qualitative data where order does not matter

• Ex: Color

Ordinal Scale

Qualitative data where order does not matter, but we can’t measure differences

• Ex: Clothing sizes, customer satisfaction scale

Interval Scale

Quantitative data where the differences make sense, but the data does not have a starting point

• Ex: Day-by-day temperature, cannot say 5% colder because no absolute starting temperature

Ratio Scale

Quantitative data where differences make sense and the data has a starting point

• Ex: Age, ranking vote averages

Frequency

Number of times a value of the data occurs

Relative Frequency

Ratio of the number of times a value occurs in the set to the total number of outcomes

Interquartile Range (IQR)

Range of the middle 50% of the data values

• Found by calculating the measure of spread

• IQR = 3rd Q- 1st Q

Variance

Mean of the standard deviations from mean, or square of standard deviation

IQR Outlier Rule

Any data beyond Q1 - 1.5(IQR) and   Q2 + 1.5(IQR) becomes insignificant

Addition Rule

OR events

Multiplication Rule

AND events

Conditional Probability

“A given B”

Discrete Probablility Distributions

Probability of individual outcomes can be greater than 0, or measured “exactly” 

• Hypergeometric

• Binomial

• Poisson

Hypergeometric

Finding the number of successes where the probability changes between each trial 

• Ex: drawing cards w/o replacement

Binomial

Finding number of successes where the probability of successes does not change between each trial

• Ex: flipping a coin

Poisson

Finding the number of events that occur over a given interval 

• Ex: calls per day

Continuous Probability Distributions

Infinite number of outcomes, measures the probability of ranges in outcomes

• Uniform

• Normal (Standard)

• Exponential

Uniform

Using the area to find the probability in a range

CDFs

Finds the probability of values to the LEFT of x

Exponential

How long is an interval between events?

• u

• Ex: average waiting time

Normal

Convert non-standard distributions into standard normal distributions, aka z-scores

Standard Normal

Z~N (u=0, o=1)

• ± 1o = 68%

• ± 2o = 95%

• ± 3o = 99.7%

Normal Standard Excel

NORM.S.DIST (True)

Poisson Excel

POISSON.DIST (False)

Binomial Excel

BINOM.DIST (False)

Hypergeometric Excel

HYP.DIST (False)

Exponential Excel

EXP.DIST (True)