Statistics Tutorial

By Xah Lee. Date: 2023-05-02. Last updated: 2023-05-06.

2023-05-02

Statistics Basics

data types in histogram

histogram. in statistics or probability chart, the histogram, there are several interpretation of the char's column values and height. the different data sets may be: data sample, population, probability distribution.

population (statistics) means the data set of all.
sample (statistics) means a subset of population. (usually randomly selected)
data set (statistics) means a set of numbers. e.g. [65 98 10 580]. Or each can be a pair, such as age and income e.g. [ [28, $77], [30, $40 ],[42, $27 ], [81, $33 ] ], or name and age e.g. [[jon, 65], [mary, 54], [joe, 565]]
probability distribution is a set of pairs of numbers. usually a event lable, and its probability e.g. throw dice, each pair [total, probability].

Central tendency

these are numbers to represent some kinda of middle, common value, or average.

Arithemetic mean. usually written as μ. is the average. i.e. sum of the values of each event, divided by total count of possible events.
Median. middle value separating the greater and lesser halfs of a data. Median of [1, 3, 3, 6, 7, 8, 9] is 6. Median of [ 1, 2, 3, 4, 5, 6, 8, 9] is (4+5)/2. The data set must have an order. Used only for 1-dimensional data. Median
mode. Most frequent value in a data set. e.g. 2 is the mode of [1, 2, 2, 3, 4, 7, 9]. Used only for 1-dimensional data.

Measure of Variation

deviation (of an event) is the difference between the event value and the arithemetic mean. (if x is value of an event, m is mean, then deviation = x-m.) Deviation (statistics)
Squared deviation from the mean (SDM) (for an event) is square of the deviation of the event. (if x is value of an event, m is mean, then squared deviation = (x-m)^2.) Squared deviations from the mean
Variance, is the average of SDM. variance is usually denoted σ^2. (if x is value of an event, n is number of events, m is mean, σ^2 = (Sum[(x - m )^2, {x,1,n}])/n.)
Standard deviation (usually denoted σ), is square root of variance. i.e. Sqrt[ (Sum[(x - mean)^2, {x,1,n}]) /n ] There is also Sample Standard deviation, which instead of divided by n, divide by (n-1). Standard deviation
the expected value is a generalization of the weighted average. Informally, the expected value is the arithmetic mean of a large number of independently selected outcomes of a random variable. Expected value

confidence interval Confidence interval

2023-05-02

BA 115 "STATISTICS" PRACTICE FINAL spring 2023

(1) Five people enter the elevator on the first floor of a 10-floor building. Each of them chooses a floor to leave the elevator at random, and each floor is equally likely to be chosen, independently of all the others. Set up a box model first.

(a) What is the chance that at least one person will get out on the second floor?
(b) What is the chance that at most one person will get out on the third floor?
(c) What is the chance that all 5 people will get out on the same floor?

(2) In order to play on a slot machine you have to insert M quarter. Then you have 10% chance of getting 3 quarters back, including your stake, which means that your net gain is 2 quarters. You have a 10% chance to get 2 quarters back, 40% chance that you get 1 quarter back and 40%Äance that you lose your stake of 1 quarter.

a) Set up a box model for your net gain. Compute the average and the SD of the box.
b) In 100 games, what are your chances of not losing money?
c) How many times do you have to play to be 90% sure that you have lost money?

(3) A survey organization wanted to find out the percentage ot women between 30 and 40 in a certain county who are working full time. They took a simple random sample of 400 women in that age bracket, and 127 turned out to work full time.

(a) Set up a 90% confidence interval for the true percentage of working women.

(4) Someone would like to find out the average rent for a one-bedroom apartment in Berkeley. In order to do that he took a simple random sample of 100 one bedroom rental units. Suppose the sample average is $1200, and the sample SD is $120.

(a) Set up a 95% confidence interval for the average rent of a one-bedroom apartment
(b) True or false: the rent for abo $80/ f one-bedroom rental units is between $1080 6820 and $1320.

(5) Results of an IQ test on a nationwide basis have been standardized in such a way that the average is 100, the SD is 20 and the histogram for the scores follows the normal curve quite closely. A school board in a certain school district chooses a simple random sample of 400 children in order to compare the performance of their children to the nationwide standard. The children in the sample scored on average 98.

(a) Is this the true difference or just a chance variation in sampling?

2023-05-01

Statistics, 4th Edition. 2007. by David Freedman, Robert Pisani, Roger Purves. Buy at amazon

worst book. verbose, and written as if you are children, and injects sjw gang stuff like court cases about sjw racism. does not explain the mathematical gist.

PART I. DESIGNS OF EXPERIMENTS
Chapter 1. Controlled Experiments
Chapter 2. Observational Studies

PART II. DESCRIPTIVE STATISTICS
Chapter 3. The Histogram
Chapter 4. The Average Standard Deviation
Chapter 5. The Normal Approximation for Data
Chapter 6. Measurement Error
Chapter 7. Plotting Points and Lines

PART III. CORRELATION AND REGRESSION
Chapter 8. Correlation
Chapter 9. More about Correlation
Chapter 10. Regression
Chapter 11. The R.M.S. Error for Regression
Chapter 12. The Regression Line

PART IV. PROBABILITY
Chapter 13. What Are the Chances
Chapter 14. More about Chance
Chapter 15. The Binomial Formula

PAR IV. CHANCE VARIABILITY
Chapter 16. The Law of Averages
Chapter 17. The Expected Value and Standard Error
Chapter 18. The Normal Approximation for Probablity

PART VI. SAMPLING
Chapter 19. Sample Surveys
Chapter 20. Chance Errors in Sampling
Chapter 21. The Accuracy of Percentages
Chapter 22. Measuring Employment and Significance Unemployment
Chapter 23. The Accuracy of Averages
PART VII. CHANCE MODELS
Chapter 24. Model for Measurement Error
Chapter 25. Chance Models in Genetics

PART VIII. TESTS OF SIGNIFICANCE
Chapter 26. Tests of Significance
Chapter 27 More Tests for Averages
Chapter 28. The Chi-Square Test
Chapter 29. A Closer Look at Tests of Significance