Statistics Lesson Notes - PDF

LESSON 1 Statistic -​ the science of collecting, organizing, analyzing, and interpreting data in order to make decision Data -​ information coming from observations, counts, measurements, or responses. Population -​ entirety of the group Sample -​ few members Parameter -​ valu...

LESSON 1 Statistic -​ the science of collecting, organizing, analyzing, and interpreting data in order to make decision Data -​ information coming from observations, counts, measurements, or responses. Population -​ entirety of the group Sample -​ few members Parameter -​ value obtained from a population Statistic -​ value from a sample Classification of Data Qualitative -​ Consists of attributes, labels, categories or non-numerical entries Qualitative -​ Numerical measurements of counts Quantitative Variable Discrete -​ result of counting Continuous -​ result of measurement Four ways of collecting data ​ Observational Study - Observes and measures part of a population ​ Experimental - a treatment is applied in part of population. ​ Simulation ​ Survey Sampling Methods Random -​ equal chance of being selected ​ Simple Random Sample - equal chance of being selected ​ Stratifies Sample - divide the population into strata and sample from each. ​ Cluster Sample - divide the population into strata and then randomly select some of the group. ​ Systematic Sample - randomly select a starting point and take every nth piece of data Non-random -​ no chance of selection, or the probability of selection cannot be accurately determined. ​ Convenience Sample - select any member from the population who are convenient and readily available. LESSON 2 Central Tendency -​ mesures, which describes the middle or the center of the data -​ it also a value to represent a set of scores or frequencies Mean (x̄) x-bar (x bar, idk) -​ most popular measure of central tendency -​ commonly called average -​ Median (md) -​ value of the middle observation in an ordered distribution -​ measures the center by dividing it into two equal parts -​ arrange first in descending (h to l) OR ascending (l to h) Mode (mo) -​ data entry the occurs with the greatest frequency -​ 0 mode: NO MODE -​ 2 mode: BIMODAL -​ 3 or more mode: MULTIMODAL Skewness in relation to central tendency ​ Skewness is a measure of the asymmetry of a distribution. ​ A distribution is asymmetrical when its left and right side are not mirror images. ​ A distribution can have right (or positive), left (or negative), or zero skewness. LESSON 3 Measure of Variability -​ aka measure of spread -​ number that measure how spread out a data set is along the axis “how far each element is from some measure of central tendency” Dispersion is the difference between the actual value and average value. (Deviation) Measure of Variability -​ Range -​ Variance -​ Standard Deviation Range -​ difference of highest value and lowest value Formula: HIGHEST VALUE - LOWEST VALUE Advantages: -​ easy to compute and understand Disadvantages: -​ can be distorted by a single extreme value Variance and Standard Deviation -​ measure the spread out the data is from the mean -​ the further the data spreads, the greater the standard deviation Problem Solving Steps: 1.​ Compute for mean 2.​ Subtract mean from value of data set (x - x̄)  3.​ Square the (x - x̄), then get the sum 4.​ Solve for the variance and standard deviation LESSON 4 Definition of Terms: -​ Sample Space is the set of all possible outcomes of an experiment. -​ Random Variable is a function that associates a real number to each element in the sample space. -​ A numerical distribution of the outcome of a statistical experiment. Classification of Random Variable: -​ Discrete Random Variable: countable outcome -​ Continuous Random Variable: value is on continuous scale Definition of Terms: -​ Probability of P(X) a measure of certainty or uncertainty that an event will happen -​ Discrete Probability Distribution, aka Probability Mass Function, is a list of each possible value of random variable together with the probability Properties of Probability Distribution 1.​ The probability of each value of the random variable must be between or equal to 0 and 1.  2.​ The sum of the probabilities must be equal to 1 Tree Diagram- graphic organizer that uses branching connecting lines to represent a certain relationship between events LESSON 5 Definition of Terms -​ Mean for discrete random variable, denoted as μ (pronounced as “mu”). -​ central value or average of its corresponding probability mass function. Definition of Terms: -​ Variance and Standard deviation describe how scattered out the scores are from the mean value of the random variable Reminder: -​ σ (sigma) Symbols of Variance: -​ Population variance- σ² -​ Sample variance- s² Symbols of Standard Deviation: -​ Population standard deviation- σ -​ Sample standard deviation- s Formula: VARIANCE​ STANDARD DEVIATION Problem Solving Steps: 1.​ Find the mean. 2.​ Subtract the mean from each value. (X - μ) 3.​ Get the square of the result obtained in step 2. (X - μ)² 4.​ Multiply the result obtained in step 3 by the corresponding probability 5.​ Get the sum of the of the results obtained in step 4.The result is the value of the variance 6.​ Get the square root of results in step 5 to get the value of Standard Value LESSON 6 Normal Distribution The graph of Normal Distribution depends on two factors: 1.​ Mean – determines the location of the center of the graph. 2.​ Standard Deviation – determines the height and width of the graph. The red curve has a larger value of standard deviation, therefore more spread-out. Properties of the Normal Curve 1.​ Bell-shaped and symmetric 2.​ Equal mean, median and mode 3.​ The total area under the curve is 1. 4.​ No limit to the left and right EMPIRICAL RULE ​ 68% of data falls within the first standard deviation from the mean. ​ 95% fall within two standard deviations. ​ 99.7% fall within three standard deviations. The Standard Normal Curve Finding Probabilities of Normally Distributed Random Variables: EXAMPLES: