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# Class Note for MATH 115A with Professor Dawson at UA

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Date Created: 02/06/15

Hi stag Math 1 1 EA Spring 2008 Dawson Summarizing Data 0 Raw data often contains information that we would like to extract To do so we organize it in various ways The steps we focus on in this section are 0 Sort the data 0 Find the minimum and maximum of the data 0 Find the range of the data 0 Compute the data s mean 0 Group the data 0 Plot a histogram Sorting Data Highlight the data cells including headers that you would like to sort a Click on the Data tab an H quuve lr clammnmw ua j 439 Cm pmesmewaam 12 p m gwmgw Gem 39 3 CODY Page Jmet Pam In 1 g m 7 3 vl Emerge a Center w l s 39 II 39 o Click on the Sort Icon 7 val v m l l H Sorting Data o The following window should appear l CCCC el 0 Under Sort by select the column label that you would like to use to sort 0 Select the appropriate values in Sort On and Order 0 To do further sorting select Add Level Minimum Maximum Once data is sorted you could read the maximum and minimum values off of the data 0 lollilNclould also use the functions MAX and These are found on the Formulas Tab More Functions Statistical 93 A Home mm Fag layout Fomlulds Data Revlew View Developev 1 l Tum u G lll whm M Mr 7 mm w E 339 G E 3 1x 2 am 59 DU 51 IE mm AuKaSum amnuy Fmanual Logmal rm Dateix magma mm 7 nmmon um nme Ramm g mg sumo n W Emma msewemun 7 mm Wm men mude mm A L m f l y inqmeermg mg l V A B c D E F El gun AVERAGE 739 inlzrmaklan v 7 A SICKLEA VE TIMES l AVERAGE l l AvEmcHFs l k build Records of henumber ofhouxs ofsick leave taken by 500 production SETleTl Range and Average The range of data is the difference between the maximum value and the minimum value o The average or mean of data can be found by using the AVERAGE function found under the statistical functions Minimum Maximum and Average Click on an empty cell where you would like the minimum maximum or average to be entered o You should enter a label for this cell so I can tell what you are calculating Insert the appropriate function I Formulas tab More Functions Statistical39 MAXMINAVERAGE Minimum Maximum and Average A window like this should appear In Number 1 enter the cells that you would like to consider 0 Leave Number 2 blank Click OK Histograms A histogram is a tablegraph that sorts data into pre specified categories or bins 39 Histograms You can find Histograms under a Data Tab 0 Data Analysis Histograms You should get the following window Data Analysis Analysls Tools lAnJva TwoFattur Wlthuut Reulxtatmn A lcmalatyan ovanance l Desolthe Statlstlcs Exponeml awning lFTegt TwoSample rm Variance FD er Analysls H1 gram 1M Averae F1 omlJube eratlun vi 0 Click on Histogram Note If you don t see the Data Analysis group in the Data tab 0 Go to Excel Options under the Office circle button in the top left click on Add Ins activate the Analysis Toolpak and Analysis Toolpak VBA Histograms Histogram Input Range is 39 I I d r You WI nee to Em Range Dem E specify the following OutputoptlonE 7 In C Qutput Range Ell Newwamshew Bin Range 0 New workbook La bels if a pplica ble Cumulatlve Percentage Elghartoutput Hisitograms Histugram 139 Input Range in Ranga Laba E Output aptuong O QutDut Range 3 New Wurksheet Ely 0 New uvkbuak E Pereto sorted histogram El umulatlve Percentage El Quart Output Input Range This is the range of cells that contains the data you want to sort Histograms Hismgram Input Input Rana 1 Labels Output apllons O Qutput Range 9 New Worksheet Ely 0 New workbook D Pgrstu sorted histogram Cumulatlva percentage D gm Output Bin Range The range of cells that contain your pre speci ed bin ranges ie your categories Bins Bins are your categories that you want to sort your data into 0 You must specify the intervals that you want 0 Example 0 Suppose you want to sort the sick hours into the categories 0 19 20 39 40 59 60 79 80 99 100 119 120 139 140 159 0 You designate the intervals by the right endpoint for each interval 0 In an empty column of Excel enter the right endpoints 19 39 etc Histograms Hismgram Input Input Range ew Worksheet Ely New workbook Pgreto Sorted hist gram Cumulative Percentage 3 gm Output Labels You MUST be consistent Check the box only if you included the column headers for BOTH the input and bins Leave the box unchecked if your ranges contain only the data and no headers H istog ra m 5 Output Range Input only the cell in which you want the Hismgram 39 output to START 12 7 You should have maul several clear columns to the right of this cell and several Eiiiilii ifil n fiim empty rows be39ow a t h i s Note Make sure you select Output Range Bins Example cont The output from Excel repeats your bin limits and gives you a frequency count how many of the cells from your input range fall in each category More should be zero If not your bin limits did not go high enough to accommodate your data Relative Frequencies Relative frequencies are the percentage of total items that fall into each bin To compute the relative frequency first count the number of records you are looking at Once the frequencies have been found in each bin take the divide each frequency by the total number of records Choosing appropriate bin limits Bins do not need to start at zero Find the range of your data Your first bin should be reasonably above your minimum data point o Your last bin limit should be greater than your maximum data point o Bins should be the same width Choosing appropriate bin limits For an initial bin size calculate the range of the data divided by 10 Make your endpoints nice numbers Each bin should be the same size 0 round your answer in step 1 if necessary o View your histogram if you are not happy with the way it looks alter your bin size Graphing the histogram Histograms are usually shown as bar or column graphs Before you insert your graph you need to make a column that contains your bin ranges that will be the labels on your graph In the Insert Tab click on Column quot Time 4r 9 Compsnlmlln Lyon2 mucmgon Excel o i m 0 a M j Header a PlVOKTEDIE Yable Plcture ND Shapes Smartr x PlE Ear Area 5atter Other Hyperlink r m v v v v Charts39 Almwm Tabla Illunrjtlans hjxti LmL Select the first type of 2 D column graph Clustered Column f Graphing the histogram Click on Select Data w chartz 31 39139 39 7 1 E Chartinqu 7 Home In 39 DeviIon l Design m L r 39x 571 JiLu rL F pangs mm JED H 35 7 I l j man Type Template CleHLanyul xi Graphing the histogram Cick Add under Legend Entries The following window appears Select Data Source Edit Series chart ism range Series game l BE Series xalues Legend Erma t Hes h 1 1 u gm gquot a 7 7 1 b1 Under Series Name type the label for what you are counting For Series Valuesquot enter the frequency cells not including the more or header men mammals Cam Graphing the histogram Cick the Edit under Horizontal Category Axis Labels The following window will appear Select Data Source chart glam range Axis Labels Legend Enmes EEnas EM 1 r E Amslebelrenge ll 7 2 In Axis label range enter the bin label ranges that you created Edda and Emutv cexs fGraphing the histogram You can create two bar graphs by adding another series 0 Click Add under Legend Entriesquot 250 200 150 100 lSick hours smk days 11 Layout 0 Once you have created your histogram you can change the format and design 5m Tmle M e 39fulx xp lwhl name 7 MmrosJ Excel hmmme sen Page Layout Formuras Data Rewew View Developer Design Layout Format Change 39 1 7 g 7 r JLLM 1quot L W 39 Ia Ii 5 i L I Chart Yule Temmate w Data 7 Type Lava haw Layout Chm 3mg Other Notes You should also be able to Compute the minimum maximum range and average of data by hand create histograms by hand interpret data given via histograms Objective Use Excel to sort data 0 Find the minimum maximum mean and range of a given data set Use the Histogram function in Excel to generate a frequency table Create a well formatted histogram in Excel Interpret a histogram

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