Chapter 2: Displaying and Summarizing Data. Excel Insert Tab Charts Group. Column and Bar Charts 8/22/2011

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1 Chapter 2: Dsplayng and Summarzng Data Part 1: Dsplayng Data Wth Charts and Graphs Copyrght 2010 Pearson Educaton, Inc. Publshng as Prentce Hall 2-1 Excel Insert Tab Charts Group Copyrght 2010 Pearson Educaton, Inc. Publshng as Prentce Hall 2-2 Column and Bar Charts Can be used for any measurement scale (nomnal, ordnal, nterval, or rato) Copyrght 2010 Pearson Educaton, Inc. Publshng as Prentce Hall 2-3 1

2 Lne Charts Useful for varables data, partcularly over tme Copyrght 2010 Pearson Educaton, Inc. Publshng as Prentce Hall 2-4 Pe Charts Useful for attrbutes to show relatve proportons Copyrght 2010 Pearson Educaton, Inc. Publshng as Prentce Hall 2-5 Area Charts Combnes features of pe and lne charts Copyrght 2010 Pearson Educaton, Inc. Publshng as Prentce Hall 2-6 2

3 Scatter Dagrams Shows relatonshps between two varables Copyrght 2010 Pearson Educaton, Inc. Publshng as Prentce Hall 2-7 Radar Chart Allows you to plot multple dmensons of several data seres. Copyrght 2010 Pearson Educaton, Inc. Publshng as Prentce Hall 2-8 Other Excel Charts Copyrght 2010 Pearson Educaton, Inc. Publshng as Prentce Hall 2-9 3

4 Ethcs and Data Presentaton Copyrght 2010 Pearson Educaton, Inc. Publshng as Prentce Hall 2-10 Contngency Tables and Cross-Tabulatons Cross tabulaton (contngency table) a table that dsplays the number of observatons n a data set for dfferent subcategores of two categorcal varables. Subcategores must be mutually exclusve and exhaustve. Age Group Gender Total Female Male Total Copyrght 2010 Pearson Educaton, Inc. Publshng as Prentce Hall 2-11 Tools for Cross Tabulaton Excel Pvot Tables PHStat Two-Way Tables & Charts Copyrght 2010 Pearson Educaton, Inc. Publshng as Prentce Hall

5 Descrptve Statstcs Frequency dstrbutons and hstograms Measures of central tendency Measures of dsperson Measures of shape Data profles Coeffcent of varaton Correlaton Copyrght 2010 Pearson Educaton, Inc. Publshng as Prentce Hall 2-13 Excel Support Excel statstcal functons Analyss Toolpak tools PHSta tools and procedures Copyrght 2010 Pearson Educaton, Inc. Publshng as Prentce Hall 2-14 Excel Descrptve Statstcs Tool Copyrght 2010 Pearson Educaton, Inc. Publshng as Prentce Hall

6 Facebook Survey Results Copyrght 2010 Pearson Educaton, Inc. Publshng as Prentce Hall 2-16 Termnology and Notaton Parameter a measurable characterstc of a populaton: μ s a parameter, x s not x represents the th observaton ndcates the operaton of addton N s the sze of the populaton; n s the sze of the sample f s the number of observatons n cell of a frequency dstrbuton Copyrght 2010 Pearson Educaton, Inc. Publshng as Prentce Hall 2-17 Arthmetc Mean Populaton Sample μ N = = 1 n N x x x = = 1 n Excel functon AVERAGE(range) Copyrght 2010 Pearson Educaton, Inc. Publshng as Prentce Hall

7 Propertes of the Mean Meanngful for nterval and rato data All data used n the calculaton Unque for every set of data Affected by unusually large or small observatons (outlers) The only measure of central tendency where the sum of the devatons of each value from the measure s zero;.e., (x x ) = 0 Copyrght 2010 Pearson Educaton, Inc. Publshng as Prentce Hall 2-19 Medan Mddle value when data are ordered from smallest to largest. Ths results n an equal number of observatons above the medan as below t. Unque for each set of data Not affected by extremes Meanngful for rato, nterval, and ordnal data Excel functon MEDIAN(range) Copyrght 2010 Pearson Educaton, Inc. Publshng as Prentce Hall 2-20 Mode Observaton that occurs most frequently; for grouped data, the mdpont of the cell wth the largest frequency (approxmate value) Useful when data consst of a small number of unque values Copyrght 2010 Pearson Educaton, Inc. Publshng as Prentce Hall

8 Mdrange Average of the largest and smallest observatons Useful for very small samples, but extreme values can dstort the result Copyrght 2010 Pearson Educaton, Inc. Publshng as Prentce Hall 2-22 Measures of Dsperson Dsperson the degree of varaton n the data. E.g., {48, 49, 50, 51, 52} and {10, 30, 50, 70, 90} Range dfference between the maxmum and mnmum observatons Same ssues as wth mdrange Copyrght 2010 Pearson Educaton, Inc. Publshng as Prentce Hall 2-23 Varance Populaton σ N 2 = = 1 ( x μ) N 2 Sample s 2 = n 2 ( x x) = 1 n 1 Excel functons VARP, VAR Copyrght 2010 Pearson Educaton, Inc. Publshng as Prentce Hall

9 Standard Devaton Populaton Sample σ s = N = 1 = 2 ( x μ) N n 2 ( x x) = 1 n 1 The standard devaton has the same unts of measurement as the orgnal data, unlke the varance Excel functons STDEVP, STDEV Copyrght 2010 Pearson Educaton, Inc. Publshng as Prentce Hall 2-25 Grouped Data: Calculaton of Mean Sample x n f x = = 1 n Populaton μ N f x = = 1 N In a frequency dstrbuton, replace x wth a representatve value (e.g., mdpont) Copyrght 2010 Pearson Educaton, Inc. Publshng as Prentce Hall 2-26 Grouped Data: Calculaton of Varance Sample s 2 = n = 1 f ( x x) n 1 2 Populaton n 2 = = 1 σ f ( x μ) N 2 Copyrght 2010 Pearson Educaton, Inc. Publshng as Prentce Hall

10 Chebyshev s Theorem For any set of data, the proporton of values that le wthn k standard devatons of the mean s at least 1 1/k 2, for any k > 1 For k = 2, at least ¾ of the data le wthn 2 standard devatons of the mean For k = 3, at least 8/9, or 89% le wthn 3 standard devatons of the mean For k = 10, at least 99/100, or 99% of the data le wthn 10 standard devatons of the mean Copyrght 2010 Pearson Educaton, Inc. Publshng as Prentce Hall 2-28 Example Mean = 28.87; standard devaton = σ about the mean: [-36.9, 94.6] 2σ about the mean: [-15.0, 72.7] Copyrght 2010 Pearson Educaton, Inc. Publshng as Prentce Hall 2-29 Coeffcent of Varaton CV = Standard Devaton / Mean CV s dmensonless, and therefore s useful when comparng data sets that are scaled dfferently. Copyrght 2010 Pearson Educaton, Inc. Publshng as Prentce Hall

11 Frequency Dstrbuton Tabular summary showng the frequency of observatons n each of several nonoverlappng (mutually exclusve) classes, or cells Relatve frequency fracton or proporton of observatons that fall wthn a cell Cumulatve frequency proporton or percentage of observatons that fall below the upper lmt of a cell Copyrght 2010 Pearson Educaton, Inc. Publshng as Prentce Hall 2-31 Example: Facebook Frends Copyrght 2010 Pearson Educaton, Inc. Publshng as Prentce Hall 2-32 Hstogram Column chart representng a frequency dstrbuton Copyrght 2010 Pearson Educaton, Inc. Publshng as Prentce Hall

12 Excel Tool: Hstogram Excel Menu >Tools > Data Analyss > Hstogram Specfy range of data Defne and specfy bn range (recommended) Select output optons (always check Chart Output Copyrght 2010 Pearson Educaton, Inc. Publshng as Prentce Hall 2-34 Examples from Facebook Survey Copyrght 2010 Pearson Educaton, Inc. Publshng as Prentce Hall 2-35 Good Practce Gudelnes Cell ntervals should be of equal wdth. Choose the wdth usng the formula (largest value smallest value)/number of cells but round to reasonable values (e.g., 97 to 100) Choose somewhere between 5 to 15 cells to provde a useful pcture of the data Copyrght 2010 Pearson Educaton, Inc. Publshng as Prentce Hall

13 Excel Frequency Functon Defne bns Select a range of cells adjacent to the bn range (f contnuous data, add one empty cell below ths range as an overflow cell) Enter the formula =FREQUENCY(range of data, range of bns) and press Ctrl-Shft-Enter smultaneously. Construct a hstogram usng the Chart Wzard for a column chart. Copyrght 2010 Pearson Educaton, Inc. Publshng as Prentce Hall 2-37 Skewness Coeffcent of skewness (CS) -0.5 < CS < 0.5 ndcates relatve symmetry Relatvely Symmetrc Postvely skewed Copyrght 2010 Pearson Educaton, Inc. Publshng as Prentce Hall 2-38 Kurtoss Refers to the peakedness or flatness of a dstrbuton. Coeffcent of kurtoss (CK) CK < 3: more flat wth wde degree of dsperson CK >3 more peaked wth less dsperson The hgher the kurtoss, the more area n the tals of the dstrbuton Copyrght 2010 Pearson Educaton, Inc. Publshng as Prentce Hall

14 Data Profles (Fractles) Descrbe the locaton and spread of data over ts range Quartles a dvson of a data set nto four equal parts; shows the ponts below whch 25%, 50%, 75% and 100% of the observatons le (25% s the frst quartle, 75% s the thrd quartle, etc.) Decles a dvson of a data set nto 10 equal parts; shows the ponts below whch 10%, 20%, etc. of the observatons le Percentles a dvson of a data set nto 100 equal parts; shows the ponts below whch k percent of the observatons le Copyrght 2010 Pearson Educaton, Inc. Publshng as Prentce Hall 2-40 Statstcal Relatonshps Correlaton a measure of strength of lnear relatonshp between two varables Sample correlaton coeffcent Covarance average of the products of the devatons of each varable from ts mean; descrbes how two varables move together Sample covarance Copyrght 2010 Pearson Educaton, Inc. Publshng as Prentce Hall 2-41 Examples of Correlaton Copyrght 2010 Pearson Educaton, Inc. Publshng as Prentce Hall

15 Excel Tool: Correlaton Excel menu > Tools > Data Analyss > Correlaton Copyrght 2010 Pearson Educaton, Inc. Publshng as Prentce Hall 2-43 Colleges and Unverstes Data Copyrght 2010 Pearson Educaton, Inc. Publshng as Prentce Hall 2-44 Box and Whsker Plots Dsplay mnmum, frst quartle (Q 1 ), medan, thrd quartle (Q 3 ), and maxmum values graphcally mn 1 st quartle medan 3 rd quartle max Copyrght 2010 Pearson Educaton, Inc. Publshng as Prentce Hall

16 PHStat Tool: Box and Whsker Plot PHStat menu > Descrptve Statstcs > Box and Whsker Plot Enter data range Choose type of data set Check box for fve number summary Copyrght 2010 Pearson Educaton, Inc. Publshng as Prentce Hall 2-46 Stem and Leaf Dsplay Each number s dvded nto two parts: x y x = stem, and y = leaf Stem = cell; leaf = value wthn cell Number Stem Leaf Stem and leaf dsplay aggregates and sorts all leaves wthn the same stem: Copyrght 2010 Pearson Educaton, Inc. Publshng as Prentce Hall 2-47 Stem and Leaf Stem unt s a power of 10; the hgher the stem unt, the more aggregaton of data Copyrght 2010 Pearson Educaton, Inc. Publshng as Prentce Hall

17 PHStat Tool: Stem and Leaf Dsplay PHStat menu > Descrptve Statstcs > Stem and Leaf Dsplay Enter data range Select stem unt or autocalculaton Check Summary Statstcs box Copyrght 2010 Pearson Educaton, Inc. Publshng as Prentce Hall 2-49 Dot Scale Dagram PHStat menu > Descrptve Statstcs > Dot Scale Dagram Copyrght 2010 Pearson Educaton, Inc. Publshng as Prentce Hall 2-50 Categorcal Data: Proportons Proporton - fracton of data that has a certan characterstc Use the Excel functon COUNTIF(data range, crtera) to count observatons meetng a crteron to compute proportons. Copyrght 2010 Pearson Educaton, Inc. Publshng as Prentce Hall

18 Cross-Tabulaton (Contngency Table) Copyrght 2010 Pearson Educaton, Inc. Publshng as Prentce Hall