# Lec1 - The first steps in understanding data Describing it...

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The first steps in understanding data … I. Frequency distributions II. Measures of center III. Measures of dispersion Describing it! Descriptive statistics tell us about the shape, center and spread of the data Inferential statistics allows us to draw general scientific conclusions from our data

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Grouped frequency distributions Creatine phosphokinase mode Right tail Left tail Skewed to the right
Areas in histograms 100% 15/36 = 42% 7/36 = 19% 16/36 = 44%

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Shapes of frequency distributions Approximation of a histogram by a smooth curve symmetric skewed to the right skewed to the left bell shaped not bell shaped bimodal
The first steps in understanding data … I. Frequency distributions II. Measures of center III. Measures of dispersion Describing it! Descriptive statistics tell us about the shape, center and spread of the data Inferential statistics allows us to draw general scientific conclusions from our data

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Descriptive statistics II: Measures of Center Mean: sum of the observations divided by number of observations Y is a variable y is the mean y = y i i = 1 n n = y 1 + y 2 + + y n n length weight rainfall concentration offspring Y is the length of a radish shoot y 1 , y 2 , y 3 , … y n are observations in a sample y 1 y 2 y 3 y 4 y 5 y 6 y 7 = 15 = 20 = 22 = 20 = 29 = 37 = 11 y 8 y 9 y 10 y 11 y 12 y 13 y 14 = 35 = 15 = 30 = 8 = 25 = 33 = 10 y = 15 + 20 + 22 + 20 + 29 + 37 + 11 + 35 + 15 + 30 + 8 + 25 + 33 + 10 14 = 22.14 mm
Deviation: difference between a data point and the mean deviation i = y i y Deviation 1 = y 1 -y = 15-22.14 = -7.14 Deviation 2 = y 2 -y = 20-22.14 = -2.14 Deviation 3 = y 3 -y = 22-22.14 = -0.14 Deviation 4 = y 4 -y = 20-22.14 = -2.14 Deviation 5 = y 5 -y = 29-22.14 = 6.86 Deviation 6 = y 6 -y = 37-22.14 = 14.86 ( y i y ) i = 1 n = 0 Sum of deviations: The mean is the center of the distribution 10 20 30 22.14 y 1 y 2 y 3 y 4 y 5 y 6 y 7 = 15 = 20 = 22 = 20 = 29 = 37 = 11 y 8 y 9 y 10 y 11 y 12 y 13 y 14 = 35 = 15 = 30 = 8 = 25 = 33 = 10

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The median Median: the middle value of the sample To calculate the median: 1. Order the observations in increasing order
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## This note was uploaded on 11/04/2009 for the course BIO 50935 taught by Professor Bryant during the Fall '09 term at University of Texas.

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Lec1 - The first steps in understanding data Describing it...

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