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# INTRODUCTORY STATISTICS CH 3 NOTES MATH 10041-007

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This 4 page Class Notes was uploaded by Marissa Nichol on Thursday September 24, 2015. The Class Notes belongs to MATH 10041-007 at Kent State University taught by Xianglan Bai in Summer 2015. Since its upload, it has received 19 views. For similar materials see INTRODUCTORY STATISTICS in Math at Kent State University.

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Date Created: 09/24/15

INTRODUCTORY STATISTICS CH 3 NOTES 31 quotarithmetic averagequot the average value Represents the typical value in a data set that is roughly symmetric Located at the balancing point of distribution of data 0 Report the mean in context ex saying the average score is between 80 and 90 0 To nd the mean add up every number and divide the answer by the number of observations 0 Z summation the value of one observation 2x this symbol means all of the values added up the number value of the different between the typical value modemost frequent and the mean average number 0 To nd variance you must square the standard deviation 0 Standard deviation is preferred over variation bc the units for variation are always squared To calculate standard deviation FOR THE POPULATION Multiply the summation by the data value minus the meansquared Divide that answer by the population The square root of that answer equals the value of the standard deviation FOR THE SAMPLE Multiply the summation by the data value minus the sample meansquared Divide that answer by the sample minus 1 The square root of that answer equals the value of the standard deviation SEE PAGE 86 FOR FORMULA ON CALCULATION STANDARD DEVIATION 32 the guideline that explains how standard deviation measures variability X SAMPLE MEAN S SAMPLE DEVIATION about 23 or 68 of the observations are in 1 standard deviation of the mean xs xs 95 of the observations are in 2 standard deviations of the mean xZs x25 o mostly all of the observations will be in 3 standard deviations of the mean x35 x35 a way of measuring a value that is relative to the sample measurements that are converted into standard units zscore does not have a unit To calculate zscore FOR THE POPULATION Data value minus the mean That answer divided by the standard deviation That answer equals the zscore 33 the middle value when all values are sorted from left to right IQR 0301 0 measures the amount of space the middle 50 of the data occupies quartiles 4 equal parts QlQZMEDlANQ3 decile divide the ranked data set from largest to smallest or vise versa into 10 equal parts 0 percentile dividing the set of data into 100 equal parts 34 The shape of the distribution of data determines the measures that are the best choice to portray the typical value and variability When it is right skewed the mean is larger than the median When it is left skewed the mean is less than the median When it is symmetric the mean is basically the same as the median The effect of outliers An outlier has a large effect on the mean but not really the median because the median isn t effected by the outlier the median is the right choice to measure the center When a graph is bimodal consider if they are representing two different groups such as male or female regarding height because they are very different Always ask if the summary of the graph makes sense 35 A distribution of data that is separated into 4 parts quartiles as Described above The length of the box on the boxplot equals the IQR vertical line in the box is the median horizontal lines called whiskers represents the entire range of data to the smallest or largest value boxplots are usually horizontal but DO NOT have to be good way to compare two or more distributions always best to use for unimodal distributions because they don t represent multiple modes well need at least 5 numbers for a boxplot observations that are farther than 15 interquartile ranges under the 1St quartile or above the 3ml quartile always investigate because it may not be an outlier the boxplot depicts the numerical summary instead of the spread of the data The 5number summary is the 1 minimum 2 Ql 3 Median 4 Q3 5 Maximum This shows potential outliers when numbers are listed next to each other

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