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# STAT 1053 Week 2 STAT 1053

GWU

GPA 3.62

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## Popular in Intro to Statistics for Social Sciences

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This 6 page Class Notes was uploaded by Morgan Routman on Wednesday January 21, 2015. The Class Notes belongs to STAT 1053 at George Washington University taught by Professor Balaji in Winter2015. Since its upload, it has received 136 views. For similar materials see Intro to Statistics for Social Sciences in Statistics at George Washington University.

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Date Created: 01/21/15

STAT 1053 Week 2 Chapter 2 Cont 12115 905 PM Numerical Summary Observations in a dataset are denoted by xsub 2 etc all the way to xsub n where in made in the sample x2 the second etc We use o in is the dataset 3 7 11 2 1 4 n6 Complete the following a Zx b ZXAZ c Zx1 d Zx 2 a Zx 3711214 26 b ZxAZ 9491214116 200 c Zx1 2610123 20 d Zx2 26A2 676 ZxAZ We want to summarize data using numerical descriptive measures 0 2 Quantities 1 9 Measure of Central Tendencies e The average of a group of numbers 0 Not appropriate for qualitative data 0 Summation of the values divided by the number of observations n o computes the mean of an entire population Is denoted using I and the total number of observations is denoted using Therefore the mean of a population would be 0 computes the mean of a sample Is denoted using an essentially an x with a small horizontal line above it this version of word doesn t have it sorry and observations are denoted using I Therefore a sample mean would be n middle value of a dataset 0 Not affected by large or small values 0 Partitions a histogram into two halves e then is the median o take the two middle numbers 0 ie 1 2 3 4 5 median is 3 1 2 3 4 23 5 52 25 which is the median n most frequent observation in the dataset The mode is represented by the peak of the histogram o The class on the histogram that holds the mode in it is called the modal class There find the mean median and mode 3 7 11 2 1 1 4 5 first reorder the dataset 1 1 2 3 4 5 7 11 a find the mean n 8 112345711 30 308 375 9 this is the mean b find the median 34 7 72 35 9 this is the median c find the mode 1 occurs twice and is hence the mode Comparing Mean Median and Mode n For a negative left skewed distribution 0 Mean lt median lt mode a For a positive right skewed distribution 0 Mean gt median gt mode a For a symmetric distribution 0 Mean median mode 2 9 Spread of the data a this is the maximum value minus the minimum value 0 Not incredibly useful 0 Can be dependent on extreme values 0 Two datasets with the same range can have different variability ie 1 2 3 4 6 10 Range 9 vs 2 5 5 5 5 11 Range 9 0 Not Robust influenced by outliers Easy to find and understand a tell the squared distance between typical observations and the mean is denoted by with N being the number of observations Where u is population mean is denoted by with n being the number of observations Where xbar is sample mean u This is the square root of the variance 0 Shows the distance between typical observations and the mean Find Variance and Standard Deviation 3 7 11 2 2 n 5 First find the mean 371122 25 255 5 Next find the variance sAZ 35 275 2115 225 225 2 wherein we subtract each observation by the mean and then square them then divide them by n1 sAZ 6251 624 sAZ 155 Standard Deviation s 2 Standard Deviation s 155 394 12115 905 PM 12115 905 PM

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