BIOl 570 1st Edition Lecture 2Outline of Last Lecture I. Introduction to course and to statisticsII. Sample (statistic), population (parameter), random samplingIII. Explanatory and response variablesIV. Observational and experimental studiesV. Categorical vs. numerical variablesVI. Displaying data Outline of Current Lecture I. Displaying data a. bar charts, histograms, cumulative frequency distributions, contingency tables,grouped bar charts, multiple histograms, scatterplotsII. Descriptive statistics a. measures of location: mean, median, mode b. measures of spread: range, variance, standard deviationCurrent LectureSingle variable:a. Numericalb. CategoricalFrequency: how many times something occurredRelative frequency: number of times out of the total, percentsBar graph- Vertical axis begins at zero Categorical - Spaces between bars- Most frequency to least OR high to lowHistogram- Vertical axis begins at zero Numerical- No spacing between bars - Labeled using mid-pointsThese notes represent a detailed interpretation of the professor’s lecture. GradeBuddy is best used as a supplement to your own notes, not as a substitute.- Looking for peaks and outliers (appears to be outside the data)Types of graphs- Uniform - Bell shaped- Asymmetric (Skewed)- BimodalTwo variables:a. 2 categoricalEx. left/right hand, male/femali. Contingency tableii. Grouped bar graphb. 1 categorical, 1 numericali. Multiple histogramsii. Cumulative frequency distribution c. 2 numericali. Scatterplot*If the bars do not begin at zero, the differences between them appear to be much larger**3D graphs are hard to read and unnecessary If we don’t have room for a graph, how can we summarize the data?1. Location: mean, median, mode2. Spread: range, standard deviation3. Sample sizeMode- most common (frequent) value, “most likely”→ modea. Unimodalb. Bimodal*not commonly usedMean4.6 4.8 5.3 5.3 6.6 (mm) Mean= 5.32 Weighted mean5 credit B (3 grade pt)2 credit A (4 grade pt)=[5(3)+2(4)]/5(2)=3.29W= weight (credits)Max allowed 1.5µg/m35.4 1.10 0.42 0.73 0.48 1.10Ȳ=1.538Median- middle point of ordered data-not sensitive to outliers (useful for screwed data set)0.42 0.48 0.73 1.10 1.10 5.4*when there is an even amount of data points, take the average**the median will not be part of the actualdata setPer capita….median NOT mean! This way half are above and half are below.Range: largest – smallest-sensitive to changes in the data↑Take average(0.73+1.10)/2=0.915Set 1: 1 4 4 4 7Set 2: 4 4 4 4 4-same mean, median and modeSet 1:1 - 4 = -3 = 94 - 4 = 0 = 04 - 4 = 0 = 04 - 4 = 0 = 07 - 4 = -3 = 9Set 2:4 - 4 = 0 = 04 - 4 = 0 = 04 - 4 = 0 = 04 - 4 = 0 = 04 - 4 = 0 = 0Yi-Ȳ (value of each individual mean)Variance- s2Set 1: s2 = sqrt (4.5) dog2 =2.12dogs Set 2:s2 = 0Standard deviation- s SD↙