# 2.3-3.4

 .remove_background_ad { border: 1px solid #555555; padding: .75em; margin: .75em; background-color: #e7e7e7; } .rmbg_image { max-height: 80px; } Stem-and-leaf diagraom or stemplot Stems - first numbers of digitsLeaf- final digits observations 30-76stems will be from 3-7arrange leafs in ascending order2 lines per stem when small amount of observations to see the distribution better1st line 3/1-42nd line 3/5-9 How to find the median of a Stemplot? Find number of observations, if even number (40) the mid point is 20 and 21.Now find in ordered stem plot from top the 20th and 21st numbers (ex. 67 & 68)Median 67+68/2=67.5 Pie charts Each piece of pie chart is a proportion of a relative frequency360*0.325(rel.freq)=117 Degree angle Bar charts similar to histograms but bars don't touch each other as in histograms Distribution shapes Bell shapedTriangularUniform or rectangularReverse J shaped J shapedRight skewedLeft skewedAll of the above are unimodal shapes - 1 pickBimodal - 2 picksMulimodal - 3 or more picksall on page 73 Population and sample distribution population distribution - can be called just distribution, comes from censussample distribution - is a a distribution of a sample data Chapter 3 Measures of Center called averages - 3 measures of center areMeanmedianmodeWhere mean and median apply only to quantitative data, whereas mode can be used in guantitative and qualitative data Mean The sum of observations devided by the number of observations Median to find median:arrange the data in increasing order. ex. 10, 22, 36,....(helpfull to use stemplot)n = # of observationsIf, # is odd, median is the observations exactly in the middle of the ordered list. ex. let n=13, (n+1)/2 --(13+1)/2=7, the seventh observation in the ordered list is the medianIf, # is even, there will be two numbers to find out use the same method, Let n=10, (n+1/2=(10+1)/2=5.5, the median between the 5th and the 6th observation. Mode The most frequent valueex. 2,5,2,4,6,2,1,2,1,2, the mode would be 2 Population mean and Sample Mean The mean of population datga is called the population mean or the mean of the variable; the mean of sample data is called a sample mean. Same terms used for median and mode. There is only one population mean and many sample means. Summation Notation Simgol (Z)Sigma- is a summation notation simbol which is shorthand for "the sum of"Summatio notation Zxi read as "summation x sub i" or "the sum of the observations of the variable x"x1+x2+x3+...123 are the subscripts used to distinquish one observation from another. Measure of variation or measures of spread descrpitive measure that indicates the amount of variation, or spread3 measures of variations:RangeSample standard deviationInterquartile range Range of data set range of data set is the difference between max and min observationsRange=Max-Min ex. Range=78-72=6in.The larger range the bigger variation The Sample Standard Deviation takes in to account all the observations, it is the preferred measure of variation when the mean is used as the measure of center. Measures variation by indicating how far, on average, the observations are from the mean.1st step is to find the deviations from the mean, that is, how far each observation is from the mean.2nd step is the sum fo squared deviations3rd step sample variance4th step is the final step in computing sample sandard deviation is to take a square root of sample variance Deviations from the mean Find mean(x bar) 1st, thento find deviation from the mean take xi and subract the mean from it x-xbar=72-75-3 The sum of squared deviations is to obtain a measure of the total deviation from the mean for all the observations we need to square the deviations from the mean. The sum of the squared deviations from th mean, Z(summation notation)(xi-xbar)2 ---called the sum of squared deviations that gives a measure of total deviation from the mean for all the observations. Sample Variance is to take an average of the squared deviations. Do so by dividing the sum of squared deviations by n-1, or 1 less than the sample size. the resulting quantity is called a sample variance - s2 write formula s2=Z(xi-xbar)2/n-1 Square root of sample varience Final step in computing standar sample deviation is to take a square root of sample varience Defining formula for Sample standard deviation (s) Computing formula for s Variation and standard deviation the more variatrion that there is in a data set, the larger is its standard deviation Section 3.3 Quartiles divide a data set into quartes (4 equal parts)the most commonly used percentiles.a data set has 3 QuartilesQ1-the number that devides the bottom 25% of the data from the top 75%Q2 - is the median, bottom 50% from top 50%Q3 - divides the bottom 75% from the top 25%1st step: arrange the data in in increasing order2nd step: determine the median of the entire data set3rd. step: determine the median of each quartile Interquartile Range IQR, is the difference between the first and third quartiles; IQR=Q3-Q1 The Five-Number Summary the five number summary of the data set is Min, Q1, Q2, Q3, Max1st: Find Min and Max observationsVariation of first quartile: Q1-MinVariation of 2nd quartile: Q2-Q1Variation for the 3rd quartile: Q3-Q4Variation of the 4th quartile: Max - Q3 Outliers observations that fall well outside th overall pattern of tha data. Can be a result of a measurement or reccording error. An unusual extreme observation Lower and Upper limits Lower limit=Q1-1.5*IQRUpper Limit: Q3 + 1.5*IQR Potential outlier observations that lie below the lower limit or above the upper limit Box-and-whisker diagram based on the five-number-summary1. determine quartiles2. determine potential outliers and the adjacent values3. Drow boxes around quarlites, and lines connection boxe and adjacent values4. Plot each potential outlier with an asterisk * Adjacent values the min and max observations Section 3.4 The population mean (mean of a variable) Same method in sample mean but different simbols.use letter M (mew)N - size of the populationwrite formula: Population standard deviation(Standard Deviation of a variable) To distinguish Population standard deviation from Sample standard deviation, the lettter is used is:o -- "sigma" the population varience>>>>>> Population Standard Deviation ( computing formula) .Square each variable and add the results........ Parameter ans Statistic Parameter: A descriptive measure for a population - and oStatistic: A descriptive measure for a sample, x and s Standardized variable z=..always has mean 0 and standard deviation 1 Standard Score (z-Score) For an observed values of a variable x, the corresponding vallue of the standardized variable z is called the z-score of the observation. Standard score is used instead of z-score.Negative z-score - observation is below meanPostive z-score - is above the mean .remove_background_ad { border: 1px solid #555555; padding: .75em; margin: .75em; background-color: #e7e7e7; } .rmbg_image { max-height: 80px; } Authorkhonka ID38627 Card Set2.3-3.4 DescriptionCh. 2.3-3.4 Updated2010-10-02T23:08:28Z Show Answers