Midterms

• Statistics - derived from Latin statisticum collegium (“council of state”)
• Statistics - derived from Italian word statista (“statesman” or “politician”)
• Al-Kindi (801-873 A.D.) wrote “Manuscript on Deciphering Cryptographic Messages” which showed how to use frequency analysis to decipher encrypted messages.
• John Graunt in Natural and Political Observations Made Upon the Bills of Mortality estimated the population of London in 1662 a
• Median - Originated in Edward Wright’s 1599 book, Certain Errors in Navigation, concerning the determination of a location with a compass.
• Further advocated by Ruder Boskovic in his 1755 book on the shape of the earth, in which he showed that the median minimizes the sum of absolute deviations.
• The term “median” was coined by Galton in 1881.
• The mean of two numbers was a well-known concept to the ancient Greeks
• Mean - Shown to minimize the sum of squared deviations by Thomas Simpson in 1755
• Jacob Bernoulli (1654-1705) who began probability
• De Moivre (1667-1754) refined Bernoulli’s bound and stumbled upon a discrete version of the normal curve as an approx- imation to binomial probabilities.
• In 1755 Thomas Simpson introduced the notion of error curves, including what are now called probability density functions. His pdf of choice was triangular
• Others proposed error curves of different shapes: semicircular (Lambert ), exponential (Laplace ), parabolic (Lagrange ), normal (Laplace , although it was not called the normal distribution until 1873).
• STATISTICS is a branch of mathematics that examines and investigates ways to process and analyze the data gathered
• Statistics provides procedure in data collection, presentation, organization, and interpretation to have a meaningful idea that is useful to business decisionmakers.
• Applications of statistics: education, government, business and economics, medicine and science, psychology, sociology and population dynamics statistics, and sports statistics
• Division of statistics: descriptive statistics and inferential statistics
• Descriptive Statistics - the totality of methods and treatments employed in the collection, description, and analysis of numerical data
• Descriptive Statistics - purpose is to tell something about the particular group of observation.
• DESCRIPTIVE STATISTICS - statistical information usually arises from samples, and that its analysis will require generalizations which go beyond the data.
• types of DESCRIPTIVE STATISTICS: Measure of Central Tendency and measure of variability
• types of Measure of Central Tendency: mean, median, mode
• Measure of Central Tendency or Position or Location - a single figure which is representative of the general level of magnitudes or values of the items in a set of data
• Measure of Central Tendency or Position or Location - a measure that determines where the group tends to cluster or to center
• Measure of Central Tendency or Position or Location - a single value which best represents the entire group.
• Mean (Me) - is an arithmetic average of all the scores in a distribution
• Mean (Me) - is the most stable, sensitive, consistent and reliable measuring instrument.
• Mode (Mo) - is the most frequent score
• Median (Md) - is the central value that divides the ordered data collection into two equal parts
• Median (Md) - is the value of the middle term after arranging the data in ascending or descending order.
• Measure of Variability - a measure which aids the statisticians in making comparisons
• Measure of Variability - is a measure which describes how far away from the mean is the score.
• types of measure of variability: standard deviation, variance, range
• Standard Deviation - is a measure of the distance from the observations in a data collection to the middle of that collection.
• Standard Deviation - describes or shows how far above or below is a score from the mean
• Variance - is the same as the standard deviation except that the square root is not taken.
• Range - is the distance between the highest and lowest score in a array of data.
• population - consists of all the members of the group about which you want to draw a conclusion
• sample - a portion, or part, of the population of interest selected for analysis.
• Inferential Statistics - the logical process from sample analysis to a generalization or conclusion about a population.