Class Notes (806,888)
MATH 203 (22)
Lecture

# cheat sheet.docx

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School
McGill University
Department
Mathematics & Statistics (Sci)
Course
MATH 203
Professor
Patrick Reynolds
Semester
Fall

Description
Descriptive data  response of just a sample (summarize & present) CHAPTER 1- 1) Identify population or sample (collection of exp.units) Statistical inference  an estimate, or prediction about a population based on a sample (generalization) 2) Identify variable(s) Population  set of units we are interested in studying; “set of all *insert sample+” 3) Collect data Sample  subset of the units in a population; a certain # 4) Describe data Quantitative data  numeric data Qualitative data  can be classified into classes TYPES OF DATA Inferential data  utilize data to make inferences about a pop. Representative sample exhibits characteristics typical of those possessed by the target population 1) Identify population (collection of all experimental units) Random sample  of n experimental units; sample selected from the population in such a way that every sample of size n has a chance of being selected 2) Identify variables 3) Collect sample data (subset of pop.) 4) Inference about population based on sample 5) Measure of reliability of inferences EX: 1) Poll on war in Iraq: inference of interest: to estimate the proportion who believed the war was justified Problems with random samples: Methods of data collection: (based on 2000 individuals called(sample), population= all US citizens) 2) Does massage enable faster recovery for tired athletes? 8 boxers(experimental units) in designed experiment. Inference drawn= having a massage does not enable muscles of boxers to recover faster. 1) Selection bias Observational 2) Non-responsive bias Publishes source No change in mean HR or blood levels  can’t make this inference about all athletes (population)  can only 3) Measurement error Survey make inferences that relates to the sample used Designed the experiment CHAPTER 2- Class frequency  # of observations in the data set that falls into a particular cBar Graph (qual)  Pareto diagram (qual) Stem and leaf (quan) Histogram (quan) Class relative frequency  class freq/n Summation notation  divided into classes des. order cannot be divided into Note: ∑ 2= distinct classes Class %  (Class relative frequency)x100 𝑛 x + x … 2 2 𝑋𝑖 𝑖= 2 2 Sample variance (S ) units= x  mode  most frequently occurring value Skeweness  right skewed left skewed symmetric 𝑛 2 ∑ 𝑖= 𝑥 𝑖 2 Standard deviation (S) units=x ∑ 𝑖= 𝑥𝑖 median (middle #)  arranged in ascending 𝑛 𝑆 2 𝑆 𝑆2 𝑛 order. Even #= mean of middle 2 #s. odd # = middle number mean  sum/n 2 2 2 2 2 2 1 2 2 EX: 1) variance , ∑ =1.53 + 1.50 + 1.37- + 1.51 + 1.55 + 1.42 + 1.41 + 1.48 =17.34 note: population mean =µ, pop. Std variance = σ,pop. Std variance = σ , therefore (µ±k σ).--> for every unit in a population 2 7 – 2 S = 7 =0.0033ppm S=0.058ppm Chebyshev’s Rule  works for all datasets regardless of shape 𝑥 𝑥̅ 𝑥 µ 𝑧 𝑠𝑎𝑚𝑝𝑙𝑒 𝑧 𝑝𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛 1) Very few measurements fall within 1 std.devs ( ̅ ̅ 𝑆 𝜎 Empirical rule  only works for symmetric mound shapes 2) At least 3/4 of the measurements fall within 2 std. dev ̅ ̅ Z-score  represents 1) Approximately 68% of the measurements fall distance between given within 1 std dev. 𝑥̅𝑠 ̅𝑥 𝑠 3) At least 8/9 of the measurements fall within 3 std. devs ( ̅ ̅ measurement and the 2) Approximately 95% of the measurements fall 4) For any #, K>1, at least (1-1/k ) of the measurements fall within k std. devs ( ̅ mean (given in std. dev), with 2 std. dev 𝑥̅ 𝑠 𝑥 𝑠 smaller z score =more likely 3) Approximately 99.7% of the measurements fall Ex: 1) given the largest value is 765 and the smallest is 135m estimate the std. dev to contribute to that group 760− 5 within 3 std. dev. 𝑥̅ 𝑠 ̅𝑥 𝑠 Using chebyshev’s rule  at least 8/9 of the measurements fall within 3 std. dev = 104= 6 𝑠𝑡𝑑 𝑑𝑒𝑣 EX: looking for students in S rd 760− 5 top 2.5% (GPA) 3 line  Using empirical rule (given its mound shaped) 95% fall within 2 std dev 𝑠𝑡𝑑 𝑑𝑒𝑣= 156=S  𝑥−2 7 z score =2, = 0 5 , using 4 std de. Because missing 5% x= 3.7 (GPA), top 16% 2)in units anaesthesia mean = 79, std dev=23. Assuming mound shape, what % of dentist use less nd than 102 units? 79+23=102  +1 std deviation  need to still uinclude all those less  50% + +2.5% + 13.5%  2 line, z- 𝑥−2 7 34% (̅𝑥 𝑠 = 84% **MEASURES OF DISPERSION:RANGE+IQR+VARIANCE+STD score = 1, = ,x= 3.2 0 5
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