USING EXCEL ON THE COMPUTER TO FIND THE MEAN AND STANDARD DEVIATION AND TO DO LINEAR REGRESSION ANALYSIS AND GRAPHING TABLE OF CONTENTS

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1 USING EXCEL ON THE COMPUTER TO FIND THE MEAN AND STANDARD DEVIATION AND TO DO LINEAR REGRESSION ANALYSIS AND GRAPHING Dr. Susan Petro TABLE OF CONTENTS Topic Page number 1. On following directions 2 2. Opening Excel 2 3. Making your table 2 a) Inserting a symbol 4 b) Inserting a 4 c) Subscripts and superscripts 4 d) Significant figures 4 e) Merging cells 5 4. Making your graph 5 a) Deciding how to set the y intercept 11 b) Adding the correlation coefficient ( r ) to your graph 13 c) Formatting your graph To change the graph title, axes labels, etc. 14 To format graph title 15 To format the axes labels 15 To format the axes numbers and axes lines 16 To format the borders 17 To format the trendline Solving for Unknowns a) To solve for x when you know y 18 b) To solve for y when you know x Formatting your table a) Centering data 20 b) Formatting table headings 20 c) Adding borders Making a Multi-line Graph Making a Histogram 22

2 9. Calculating the Mean Calculating the Standard Deviation How to embed an Excel graph and tables into a Word document Examples of Graphs a) Single Line Graph 28 b) Multi-line Graph 29 c) Histogram 30 On Following Directions From We Took to the Woods by Louise Dickinson Rich I m a good knitter, and I m proud of it. I can make up my own directions, or I can follow printed directions, which apparently is the harder thing to do, although I don t see why it should be. I think the difficulty with people who can t follow printed directions for knitting or anything else is that they try to understand them. They read the whole thing through and it doesn t make sense to them, so they start with a defeatist attitude. They try to relate the first few steps to the whole, and there is no obvious relation, so they get discouraged and say, Oh, I can t learn things out of books. You don t have to understand directions. All you have to do is follow them; and you can follow them only one step at a time. What you need is not intelligence, but a blind faith. I never read directions through. I never read beyond the operation I am engaged in, having a simple trust that the person who wrote them knew what he was doing. That trust is usually justified. Oh, there s no trick to following directions, and if I don t teach my children one other thing, I m going to teach them that. I think it s important. Opening Excel Click on start at the bottom left of the screen. Click on Programs. Click on MSOffice. Click on Microsoft Excel. Making your Table Decide what data should go on the x axis (the determinate axis) and what data should go on the y axis (the indeterminate axis). The information you knew before you ran the experiment goes on the x axis and the information you got by doing the experiment goes on the y axis. For example if you are measuring the absorbance of a number of dye concentrations the dye concentrations will be on the x axis since you decided on and prepared what concentrations you wanted to test. You didn't know what the absorbances 2

3 would be until you put the various concentrations in the spectrophotometer, so absorbance would go on the y axis. Type in the heading for the x axis in the A1 box e.g. concentration (mg/ml). If the heading is too long to fit in the box, you may increase the column width by placing the cursor on the line between A and B so you get a double headed arrow and dragging to the width you want. To have your data in columns To have your data in columns, type in the heading for the y axis e.g. absorbance in the B1 box. To have your data in rows To have your data in rows, type in heading for the y axis e.g. absorbance in the next box in the column, A2. Remember your page width only goes through I so if you have rows to the right of I they will not show up on your page when you print it. Also if you have increased the width of a column, your page width will not go as far as I anymore. Enter the values for x (numbers only, no letters or symbols) in the A column under your heading if you are doing your data in columns. Enter values for x in the 1 row following your heading if you are doing your data in rows. For data in columns, enter values for y (numbers only, no letters or symbols) under the y axis heading e.g. enter values in B2, B3, etc. For data in rows, enter values for y in boxes to the right of your y axis heading e.g. B2, C2, D2, E2, etc. 3

4 DO NOT enter values for your unknown in the table at this point. Inserting ( ) symbol To insert a degree ( ) symbol hold down the Alt key and type 248 on the number pad. (If you are using a Macintosh computer hold down Alt key, shift key and hit the number 8 key.) Inserting a symbol To insert a symbol open up a word document. Click on insert on the task bar. Click on symbol. Find the symbol on the table and select it. Click on Insert then click on Close. Now select the and click on Edit on the task bar. Click on cut or copy. Open your Excel document and click on Edit and then Paste. Subscripts and Superscripts To insert a superscript or subscript in Excel click on Format on the menu bar. Then click on Cells. A window will open. In the lower left of the window it says Effects. Click on the box to the left of subscript or superscript. A check mark will appear. Now click on OK. Type in the superscript or subscript. To exit super/subscript mode, repeat the process above. When you click on the box with the check mark it will disappear. Click on OK. Significant figures To have all your data values have the same number of spaces to the right of the decimal point select all the cells containing numbers. Click on Format. Click on Cells. Click on Number. Click on Number under Category. Decide the number of spaces you want to the right of the decimal point based on the significant figures you used for your measurements. Click on OK. 4

5 Merging Cells To merge cells select the cells you want to merge and then click on the merge icon on the toolbar Making your Graph Select the entire table including the headings. Click on Chart Wizard on the standard toolbar (top row of icons). This icon looks like a multi-colored bar graph. Chart Wizard Step 1 of 4 - Chart Type will appear. 5

6 Click on XY (Scatter) line under Chart Type. Under Chart subtype click on the top chart if it is not already selected. Click on Next. Chart Wizard Step 2 of 4 - Chart Source Data will appear. If the data in your table is in columns click on columns, if it is in rows click on rows 6

7 Click on Next. Chart Wizard Step 3 of 4 - Chart Options will appear. 7

8 On the Title card enter chart title (e.g. The Effect of Concentration on the Absorbance of Methylene Blue Dye at a Wavelength of 675nm). Enter X axis title e.g. Concentration (mg/ml) of Methylene Blue Dye. Enter Y axis title e.g. Absorbance (Abs units) of Methylene Blue Dye. Click on Next. Chart Wizard Step 4 of 4 - Chart Location will appear. You must decide if you want your chart as a new sheet or as an object on the sheet with your table. For Fundamentals of Biology have the table on the same page as the graph for ease in correcting so click on as an object in the sheet. Click on Finish. 8

9 Click on the chart area. Small boxes will appear along the borders. Click on the white area of the graph so a four-sided arrow appears. Holding down the left mouse button, drag the chart below your table. Now click on one of the small boxes on the bottom edge of your graph so a double-sided arrow appears. Drag the bottom of the graph down to number 48. Click on one of the small boxes on the right side of your graph so a doublesided arrow appears. Drag the right side of the graph to the letter I in width if you haven t increased the size of the cells. Double click on the plot area. Format Chart Area dialog box will appear. To change the background color of the plot area click on the box under Area that is the color you want. I prefer a white background for maximum contrast so click on none. Click on OK. Click on one of the points on your graph. All the points in the line to which that point belongs will become larger squares. 9

10 Click on Chart on the menu bar. Click on Add Trendline. Click on Linear box if it is not already highlighted. Click on Options card behind Type card. 10

11 Deciding how to set the y intercept Click on Set Intercept when dealing with linear regression data where y was zero when x was zero for example in labs using the spectrophotometer to measure absorbance. (The spectrophotometer is blanked; set to zero absorbance at zero concentration of the substance whose absorbance is to be measured.). Otherwise don t click on Set Intercept. Set Intercept will set the y intercept at zero so when your formula (y = bx + a) comes up the a value will be zero and not appear. Click on 'Display equation on chart'. The formula y = bx + a with appropriate values for b (slope) and a (y intercept) will appear on your graph Click on 'Display R-squared value on chart'. R 2 is the correlation of determination. Values for the correlation of determination range from zero to one. The higher the correlation of determination (the closer to one) the better the regression line is in explaining the variation of the data. 11

12 Click on OK. To move formulas where they can be more easily seen, click on the formula. A hatched border will appear around the formula. Click on the border and drag it where you want it. 12

13 The default point size of the formulas is quite large so to change the point size, click the down arrow next to the displayed point size in the Formatting toolbar and choose a smaller point size. To add the correlation coefficient ( r ) to your graph: If your graph is on the same sheet as your table, click in any empty cell to the right of your graph. A heavy border will appear around the cell. Type in =sqrt(the R 2 value from your graph) e.g. if R 2 was then type =sqrt(0.949). Hit Enter. The r value will appear in the cell. Now click on the graph so the hatched border appears around the plot area of the graph and the word Plot Area appears in the Name box. Click in the formula bar that is to the right of the Name box. Three icons will appear. Now type in r = whatever you got above e.g. r = If your slope value (b) was positive the r value is positive, if the slope value was negative then the r value will be negative. So if your slope was negative type a negative sign in front of your r value. Click on the green check mark icon. What you typed will appear on your graph surrounded by a hatched box. To change the point size of the r value click the down arrow next to the displayed point size in the formatting toolbar and choose a point size to match your formula point size. Drag the box so it is under your other formulas. 13

14 The correlation coefficient indicates how closely the points on your graph fit a straight line. A value of +1 or -1 indicates a perfect direct or indirect relationship between x and y. If your correlation coefficient is not close to +1 or -1 your data is not linear (Perhaps it is logarithmic, exponential or polynomial). If this is the case you wouldn t use linear regression for graphing your data. A correlation greater than 0.8 is generally described as strong, whereas a correlation less than 0.5 is generally described as weak. Note that the correlation coefficient indicates a relationship between the variables of interest. This does not necessarily imply that one variable causes the other (for example, higher SAT scores do not cause higher college grades), but that there is some significant association between the two variables. Sometimes as you are working on the following formatting the r = equation will seem to disappear from your graph. Click on the spot where the equation was and it will reappear. Formatting Your Graph In the cell above your graph's upper left corner type in the Figure number of the graph. If it is the first graph in your lab report for example label it Figure 1. To change the graph title, axes labels, legend titles on a multi-line graph etc. Click twice on the item to be changed. (Note : This is not a double click, but two separate clicks.) The cursor will appear and you can make your changes. Alternatively Click on the item you want to change. A hatched border will appear around it. 14

15 Put the cursor in the formula bar that is to the right of the Name box. Three icons will appear. Type in the corrections you want to make. Click on the green check mark icon. To format the title Double click on the title. A Format Chart Title dialog box will appear. Click on Font. Choose the size you want. Alternatively Click on the title. A hatched border will appear around the title. Click on Format. Click on Selected Chart Title. Click on Font. Choose font, font style and size you want. To format the axes labels Double click on the axis label. A Format Axis Title dialog box will appear. Click on Font. Choose the size you want for your axis label. 15

16 Alternatively Click on the axis label. A hatched border will appear around the label. Click on Format. Click on Selected Axis Title. Click on Font. Choose font, font style and size you want. To format the axes numbers or axes lines Put the cursor on the axis whose numbers you wish to format. If the cursor is correctly positioned over the axis it will read Value (X) axis or Value (Y) axis. Double click on the axis line. A Format Axis dialog box will appear. Click on Font. Choose the size you want your axis numbers to be. Click on Patterns. Choose the weight you want for your axis line. Alternatively Place the cursor as above and single click. Handles will appear on each end of the axis line. Click on Format. Click on Selected axis. Click on Font. Choose font, font style and size you want. 16

17 To format the borders To remove borderlines you don't want e.g. the border around the legend or around the plot area or around the entire graph. Double click on the area inside the border. A Format dialog box will appear. On the Patterns card click on None under Border. To format the trendline The default line is quite thick so you may want to choose a lighter weight line. Double click on the trendline. A Format Trendline dialog box will appear. On Patterns click on the down arrow beside Weight and choose the thickness you want for your line. Alternatively Click on the line. Handles will appear on each end. Click on Format. Click on Selected Trendline. Click on Weight and choose the line you want. 17

18 ATTENTION: Click outside graph and scroll back to your table. Solving for Unknown x or y To solve for x when you know y. Type in the word unknown in the empty space at the end of the y column. If your data is in columns enter the y value you got for the unknown in the box below the one where you typed unknown. This is so the instructor knows this is where you calculated your unknown. Move pointer to the empty space at the end of the x column. Type in the word 'unknown'. Now move pointer to the box below the one where you just typed unknown. Type = then a parenthesis then the y value you just entered. (If the number is very long you can just type the letter and number of the cell e.g. D11 to save time.) Now type - then the a value (y intercept) from the formula on your graph and a closing parenthesis. If your y intercept was zero you only need to type the y value without parentheses. Now type in / and the b value (slope) from the equation on your graph. Suppose the equation on your graph is y = x. This would mean a (the y intercept) is zero since it doesn t appear and b is You would type in =D11 or the number in the D11 cell/ Then hit Enter and that will give you the x value at that y. To solve for y when you know x. Type in the word 'unknown' in the empty space at the end of the x column. 18

19 Now enter the x value for the unknown in the cell below the one where you typed unknown Move pointer to the empty space at the end of the y column. Type in the word 'unknown'. Now move the pointer to the box below the one where you just typed unknown in the y column. Type = then type a parenthesis then the b value (slope) from the equation on your graph, then * and the x value you just typed under 'unknown' in the x column. (If the x value is very long you may type the letter and number of the cell containing the x value you just entered e.g. A12) Now type the closing parenthesis then + then the a value (y intercept) from your graph. Hit Enter and that will give you your y value for that x. If you set the y intercept to zero you only need to type = followed by the b value then * and the x value and hit enter. Suppose the equation on your graph was y = x You would type =(-0.421*A12) Formatting Your Table At this point number your table. Click cell A1 and then click on Insert on the menu bar. Click on Row and a row will appear above your table. Type in the number of your table. For example if this is the first table you've done for a lab report label the table Table 1. 19

20 Centering Data Select the entire table. Click on the Center icon or Click on Format on the menu bar. Click on Cells Click on card heading that reads Alignment. Click Center under Horizontal. Click OK. Formatting Table Headings Select just the table headings. Click on the B (bold) icon if you want the table headings bold. Click on Format on the menu bar. Click on Cells. Click on card heading that reads Font. Choose font, font style and size you want. Click on OK. If you want to add borders Highlight the entire table. Click on Format on the menu bar. Click on Cells. Click on card heading that reads Border. 20

21 Click on Outline and Inside boxes. Choose a style for your borderline. Click in that box. BEFORE PRINTING YOUR GRAPH be sure to click outside the graph area itself. Otherwise only the graph and not the accompanying table will be printed. To see what your graph will look like prior to printing, click on File and click on Print Preview. See an example of a single line graph on page 27 of this handout. MAKING A MULTI-LINE GRAPH Say you want to chart several lines on the same graph - for example the effect of temperature on the calories of energy consumed by several bird species say the English sparrow, the purple finch and the pine siskin. Type in heading for x axis data in the A1 cell - Temperature ( C). Say you wanted your data in rows. In the A2 cell type in Calories English sparrow, in the A3 box type in Calories purple finch and in the A4 cell type in Calories pine siskin. Your temperature values will be typed in the 1 row e.g. B1, C1, D1, etc. The calories for the English sparrow will be typed in the 2 row e.g. B2, C2, D2, etc. The calories for the purple finch will be typed in the 3 row e.g. B3, C3, D3, etc. The calories for the pine siskin will be typed in the 4 row e.g. B4, C4, D4, etc. Select the table Follow directions using Chart Wizard as previously explained. The only difference is that you must repeat the "Click on one of the points on your graph" sequence for each line. When one has several lines the formulas may be crowded and it may be difficult to see which formula goes with which line so click on the formulas one at a time and drag them away from the lines. Make titles for each formula by clicking on the graph so a hatched border appears around the plot area of the graph and the word 'plot area' appears in the Name box. Put your cursor in the formula bar to the right of the Name box. Three icons will appear. Now type in the legend title for that line e.g. English sparrow. 21

22 Click on the check mark icon. What you typed will appear on your graph surrounded by a hatched box. Drag the box so it is above the formulas for that line. Repeat for the remaining lines. To put the symbol used for each line next to the title above each formula you will have to draw it in by hand after you print the graph. The computer will choose different colors for the points of each line. If you are not using a color printer the light colors will show up poorly when printed by a black and white printer. Double click on one of the points of the trendline whose marker color you want to change. A Format Data Series dialog box will appear. Click on Patterns. Under Marker click the down arrow next to Foreground. Click on black on the pop-up palette. Now click on the down arrow next to Background. Click on black on the pop-up palette. Click on OK. See an example of a multi-line graph on page 28 of this handout. HOW TO MAKE A HISTOGRAM USING EXCEL To have your histogram bars represent ranges Below are the water volume measurements for the histogram at the end of this document. These were used to make a histogram with five equal bars. Water volume (ml) Mean = Standard deviation = ±1.25 To get five bars (or any other number you want) on your histogram: Subtract lowest value from highest. For the numbers above that would be = Now divide your answer by number of bars you want. If you want three bars divide by 3. Since we want five bars for the example divide as follows: 4.89/5 = Add this number to your lowest value to get your first range. So = The first range is thus

23 For the second range begin with 36.77, because if you use and one of the measurements happens to be exactly that you won t know whether to count it in the first range or the second range when you determine the frequencies. Now add 0.96 to the end of the first range value (36.76) to get the upper value of the second range. Second range is thus Third range is and so on. Follow previous directions for making a table. Put range values (or individual numbers depending on the type of histogram) in first column and frequencies in second column. If your x values are not ranges but single numbers, select only the y column of the table. Click on Chart Wizard. Chart Wizard Step 1 of 4 - Chart Type will appear. Click on Column box. 23

24 Click on upper left chart under subtype if it is not highlighted already. Click on Next. Chart Wizard Step 2 of 4 - Chart Source Data will appear. Click on columns if your data is in columns, click on rows if your data is in rows. Click on Next. Chart Wizard Step 3 of 4 - Chart Options will appear. Enter Chart title and label x and y axes. Click on Legend if you want the legend somewhere other than to the right. Click on Next. Chart Wizard Step 4 of 4 - Chart Location will appear. If you want the chart as a new sheet, click on 'as new sheet'. If you want it as an object in the same sheet click on 'as an object' Click on finish. 24

25 How to format your histogram. Double click on the plot area of your graph. Format Plot Area will appear. Click on 'none' under Area so background will be white. Click on one of the bars of the graph. Handles will appear on all the bars. Click on Format. Click on Selected Data Series. Choose a color for the area inside the bars. Don't click on OK yet. Click on Options. Set overlap at zero and gap width at 10. Click OK. To format the title, legend, axes and the table, see the directions for a single line graph. How to Insert a Mean and Standard Deviation Line on your Histogram First you need to have the Draw Toolbar visible. Click on View on the Menu Bar Click on Toolbars Click on Drawing. Draw Toolbar will appear. Click on the straight line icon \ on the Draw Toolbar. Draw a vertical line above where the mean would fall. Click on the straight line icon again to draw a horizontal line from the minus to the plus end of the standard deviation range. Click on the straight line icon to make the end bar for each end of the horizontal line. To add the mean and standard deviation values above the line click on the graph so the hatched border appears around the plot area of the graph and the word Plot Area appears in the Name box. Click in the formula bar that is to the right of the Name box. Three icons will appear. Type in your mean ± standard deviation as calculated using directions below. Click on the green checkmark and then drag your value over the line you made. An example of a histogram is on the final page of this handout. 25

26 HOW TO CALCULATE THE MEAN (AVERAGE) USING EXCEL Enter Microsoft Excel as previously described Type in heading e.g. water volume in ml in A1 box Enter values in A column Skip down a few rows in A column and type in Mean Go down to next row and type in =average(range of boxes containing your data) and hit Enter key e.g. if you entered data in box A2, A3, A4, A5, A6 you would type in =average(a2:a6) OR after the first parenthesis simply highlight all the boxes containing the data and the range will appear automatically. Add the closing parenthesis and hit Enter. HOW TO CALCULATE THE STANDARD DEVIATION USING EXCEL The standard deviation is a measure of the variability of your data. It describes a range within which 68% of your values lie. For example if you were weighing tomatoes and got an average tomato weight of 100grams with a standard deviation of ± 5grams, it would mean that 68% of the tomatoes you weighed were between 95 and 105 grams. Follow all directions for mean as above. Now skip down a couple rows in column A and type in Standard Deviation. Go down to the next row and type in =stdev(range of boxes containing your data) and hit Enter. E.g. if you entered data in boxes A2, A3, A4, A5, A6 you would type in =stdev(a2:a6) and hit the Enter key OR after the first parenthesis simply select all the boxes containing the data and the range will appear automatically. Add the closing parenthesis and hit Enter. To insert a ± sign in front of your standard deviations move the cursor down one cell, hold down the Alt key and type 241 on your number pad. If you are using a Macintosh computer hold down the Alt key, the shift key and hit the + key. Now type in the standard deviation value you obtained. HOW TO EMBED YOUR EXCEL GRAPHS AND TABLES INTO A WORD DOCUMENT Open your Excel file Select the table and graph Click on Control C or Edit/Copy Now open Paint. To do this: Click on Start at bottom left of your computer screen 26

27 Click on Programs Click on Accessories Click on Paint To open you Excel document in Paint Control V or Edit/Paste Now Control C or Edit/Copy Now open your Word document and when you come to the space where you want to add your Excel document Control V or Edit/Paste To save Click on File Click on Save 27

28 Table 1 Concentration (mg/ml) Absorbance (Abs units) unknown unknown Figure 1 Effect of Concentration on Absorbance of New Methylene Blue Dye at a Wavelength of 675 nm Absorbance (Absorbance units) Absorbance (Abs units) y = x R 2 = r = Concentration of New Methylene Blue Dye (mg/ml) 28

29 Table 2 Temperature ( C) Calories English sparrow Calories purple finch Calories pine siskin Figure 2 Effect of Temperature on Calories of Energy Consumed in the English Sparrow, Purple Finch and Pine Siskin Calories English sparrow Calories purple finch Calories pine siskin 25 Calories English sparrow y = x R 2 = r = Purple Finch y = x R 2 = r = Pine siskin y = x R 2 = r = Temperature ( C) 29

30 Table 3 Water volume (ml) Frequency Figure 3 Class Frequencies of Water Volumes ± Frequency Frequency Water Volumes (ml) 30

31 31