BIOM 121 1nd EditionExam # 1 Study Guide Lectures: 1 - 6Lecture 1: Statistics and Sample (August 27)Lecture 2: Displaying data and Descriptive Statistics (August 29)Lecture 3: Describing data (September 3)Lecture 4: Estimating with uncertainty (September 5) Lecture 5, 6, &7: Probability (September 10,12 & 19)Response variable: what interests us, what we measureExplanatory variable: what we are comparing, what might be predictedRelative frequency: number of times out of the total; proportion, percentTable Graph Descriptive statistic Numerical- quantitativeContinuous- ex. Mass, height, areaDiscrete- countFrequency table Histogram (labeled using mid-point, no spacing, start at zero, looking for peak/outliers)Box plotCumulative freq. distrib(2 variable: scatterplot)Location (mean, median, mode)Spread( st dev, variance, range) –SD,v2, IQRCategorical- membership in a groupOrdinal- can be orderedNominal- no ordering (religion)Frequency table(2 variable: contingency table, grouped bar graph)Bar graph (vertical axis begins at zero, spaces between bars, most frequent to least)proportionsMode: most common valueMean: average of dataMedian: middle point of ordered data (resistant) Range: largest- smallest (non-resistant) Variance: s2=Standard deviation: s=Empirical rule: if data is roughly bell-shaped thenY± 1 SD will include 67-68% of data, Y± 2SD will include 95% of dataCoefficient of variation= IQR= Q3- Q1, 50% of dataMedian: Q2Box plot: Q1 to Q3 with a line for Q2, whisker from max to min, outliers represented as dotsOutlier: data that either 1) exceeds Q3 + 1.5(IQR) or 2) is smaller than Q1 – 1.5(IQR)Graph: mean (height of bar), st dev (length of line)Point estimate: a single best guess of the value of a parameterError: difference between our estimate and the population parameter valueStandard error (SE) = Confidence interval (95%): Y – 2SE < µ < Y + 2SESample space: the set of all possible outcomes of a random trial S = { }Rule # 1: 0 ≤ Pr(E) ≤ 1, cannot be negativeTwo events are mutually exclusive if they couldn’t occur on the same trial. Rule # 3: If A and B are mutually exclusive then: Pr(A or B) = Pr(A) + Pr(B)…..”or” = ADDRule # 4: general addition rule: Pr(A or B) = Pr(A) + Pr(B) - Pr(A and B)… joint probabilityRule # 5: Pr(not A) = 1 - Pr(A)Independent: If knowing that one event occurs tells you nothing about the probability of asecond event, then the two events are independent of each other.Rule # 6: If A and B are independent: Pr(A and B) = Pr(A) Pr(B)….”add”= MULTIPLYPr(A|B) = Pr(A|not B) = Pr(A) if A and B are independentRule # 7: The general multiplication rule: Pr(A and B) = Pr(A) Pr(B|A) = Pr(B) Pr(A|B)Rule # 8: Bayes' theorem= Rule # 9: Law of total