# 0 Introduction to Data Analysis Using an Excel Spreadsheet

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3 Table 1- This shows what to put in various cells in the spreadsheet A B C D E F G 1 text =3*2 mass 2 15 =2*A2 3 =A2+1 =2*A3 4 Table 2- This shows what the spreadsheet displays A B C D E F G 1 text 6 mass The formula in cell B2 is different. It says =2*A2. What this means is twice the value of the cell A2. Since A2 is currently 15, B2 displays the value 30 (see Table 2).Cell A3 has a similar formula =A2+1, so it shows 16. One of the spreadsheet s greatest advantages can be seen when the number 15 is changed to 20. Automatically, B2 gets changed to 40 and A3 gets changed to 21. Also B3 would become 42. Another really convenient feature of spreadsheets is the ability to replicate formulas. As an example, suppose that you wanted to extend the above spreadsheet so that the numbers go from 15 and 16 all the way to 25. Of course you could type 17, 18, into cells A4, A5 etc., but this is unnecessary. Instead, you can use the copy and paste tools to replicate the formula in cell A3 to the cells A4 to A12. Cell A3 has the formula =A2+1 in it. Now what you would like in cell A4 is not exactly the same formula as A3, but you would like it to say A3+1 (not A2+1). This way it will become 17. When you tell the spreadsheet to copy and paste a formula, the formula is automatically changed in just this way. If you copy the formula A3 and paste it into cells A4 through A12, the formulas will become =A3+1, =A4+1, =A5+1 etc. all the way to A11+1. If you were to copy the formula in B2 and paste it into C2, it would change in a similar manner. It would change from =2*A2 to =2* B2, and in your example the value would become 2*(2*15) or 60. The key thing to realize is that you rarely have to type a formula more than once, even if it is used frequently. Also if you have a row of formulas and you want to change it, you can make the change once and copy it to all the other cells. Similarly if you change the number 15 in A1, all the numbers below it change. Sometimes you will want to copy a formula, or move it from one place to another, without having it change. There are a several ways to do this in Excel. The simplest way is to use 7

5 EXCEL lets you have many worksheets in the same notebook which can all be connected to one another. Small tabs on the bottom of the page let you switch from sheet to sheet (see Figure 1). It is also possible to have more than one notebook open at the same time and the window menu at the top of the sheet lets you toggle between notebooks. Entering Information To enter information (text, numbers, formulas) into a cell, move to that cell and type the information. When you start to type in a cell, whatever you type appears in the cell and also on the top left of the page in the formula bar or display line (see Figure 1). If you press enter after typing something, it will enter it on the sheet; or if you press the escape key, it will abort the entry and leave the cell unchanged. When you are entering an expression in a cell, you can edit that expression by moving the mouse to the spot you want to change (on display line). Pressing enter or moving the cursor to another cell enters the expression. If you want to change a previously entered expression, you can move to the cell and retype the whole thing or move the mouse to the display line, click the left mouse button, and then revise the expression. Entering Text You will need to put labels on your data to make your spreadsheet understandable. It is really simple to set up nice looking labels. Just type words into a cell and they will show up in the cell. For example if you type text in cell A1, it will show up. If the text is longer than the cell width (which is adjustable) the whole text will show up if there are empty cells to the right of the cell with the text in it. If the string is long and the cell to the right occupied, the string will show up cut off - but it is all still there. Entering Numbers Numbers are simply entered in a cell. A number like 15 can just be typed and its value is entered in the cell. If the number is negative just start it with a minus sign. Entering Formulas Formulas always start with an equal sign. A formula can be simple numeric expression such as =2*3, or it can include more complicated expressions involving other cells and statistical and mathematical functions. A formula like =2*B5^3 follows the rules of programming where this means 2 times the contents of cell B5 raised to the third power. Use parentheses in a natural way - for example, you can write: =1/((1/B3)^2+(1/B4)^2)^(0.5)) The spreadsheet has numerous mathematical functions such as sine (=SIN), cosine (=COS), and square Root (=SQRT), which are almost the same as in a normal mathematical expression. =SIN(C3) takes the sine of the contents of cell C3 (the angle must be in radians). Many other functions exist. The list of available functions can be viewed by clicking on the function button fx (see Figure 1) and choosing all. Functions, such as the sine, take normal numerical arguments. Some statistical functions take lists of cells or a range of cells. An example of this type of function is the average. The average function will compute the average of a list of numbers or the average of the numbers in a list of cells. So if you enter =AVERAGE(5,6,7,8) the value of the cell will be 6.5. This type of function is most useful when you give it a list of cells. If you wish to find the average of a 9

6 column of numbers that are in say cells A1 to A20, we just enter =AVERAGE(A1:A20). Most spreadsheet functions are smart so that if your range includes empty cells, they are not counted in the average or other statistical function. (Note: there is a distinction between empty and zero.) Pointing at Cells When you first start using a spreadsheet, you may often find yourself typing cell numbers into equations and expressions. All this typing is unnecessary and can lead to errors. The easiest way to put a cell number into an expression is to click on the cell, or point at it. For example, suppose that you have a number in Cell A3 and are writing an expression in which you want the cosine of the number in Cell A3. Simply type =COS( then move the mouse or cursor to cell A3 using the page up/down/left right buttons or by clicking on the cell. Then the expression you are typing will look like =COS(A3. At this point do not press enter because you have not completed the expression. Just type the closing parenthesis and then hit enter and you will have =COS(A3). Selecting Ranges You can also point at groups of cells. This is useful for functions such as the average or standard deviation that expect ranges as arguments. It is also useful when you want to mark a region that needs to be moved or copied. Anytime you need a range of numbers, use the mouse to move the cursor to the first cell in the range and hold down the left mouse button. Now drag the cursor to the last cell in the range and release the button. You should now have the range highlighted and displayed in the display line. Copying a formula Suppose you have a column of numbers in cells D2, D20, and you wish to evaluate the sine of each number (see Figure 2). To begin, enter the numbers into D2 to D20. Next in cell E2 enter the formula =SIN(D2). Now copy the formula to the entire range E2,...E20. To do this put the cursor on E2 and press the copy button (on the keyboard type either Ctrl-C, or move to the menu, click on edit and select copy). Now it expects a cell or range to be the object to be copied. Use the techniques described above to select the output range E2,...E20. (It is OK to copy the formula onto itself). Hit enter and your formula will be replicated over the entire range. Note that in cell E2 the formula is =sin(d2), but in cell E3 it has been updated to =sin(d3) rather than Sin(D2). This smart copying by Excel is very useful and leaves you with column E with the Sine of the values in column D, in just the way you would want. There is another type of copying where the cell location does not change. To fix a cell location so that it does not change in copying, you can put a \$ in front of the cell name, e.g. \$B\$1. Note that there are two dollar signs in this expression, because it is possible to fix the column and row or both so that they do not change when you copy. An example where you might want to use this is: You have a column (A1,...A20) of measured accelerations, and you want a column of forces and all objects have the same mass. If the mass is in cell D1 your formula in B1 might be =A1*\$D\$1. This way when you copy the formula to B2 it will be =A2*\$D\$1. If 10

8 other types of plots can fool you into thinking that they are plotting (x,y) points, but they are not. For example, a closer look at a Line plot reveals that it actually plots the y-values versus the order in which they are given. To be clear, you should only use Scatter plot for all of your plotting - never use a Line plot or a Bar chart or any of the other types of charts. Another problem with plotting in Excel is that it is not so easy to find what you want in all of the menus and submenus that you can access for changing a plot. The best thing to do is play around with Excel and after a while you will start to get a feel for where everything is and what the various buttons do. Fitting Data The spreadsheet allows you to do least square fits to data. To see how this works, make some data that follows a linear trend by copying the same numbers you have in column D into column F and label them with T for time. Next enter =2*F2+1 into cell G2 and copy this down into cells G3 to G20. Excel has built-in functions that use a least square fit to determine the slope and intercept that best fit a set of data. To determine the slope, go to H2, and enter Figure 2. Scatter plot of Sin(x) versus x. Note that the chart was clicked on and this caused Excel to highlight the x and y columns being plotted and display the Chart Tools menu. =SLOPE(G2:G20,F2:F20). To determine the best estimate for the intercept, enter into cell H3 the formula =INTERCEPT(G2:G20,F2:F20). Using these slope and intercept values, you can easily calculate the best estimate for the y value for any given x value. Another way to fit a straight line to a set of data is to perform a least square fit. To do 12

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