# San Jose State University Engineering 10 1

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1 KY San Jose State University Engineering 10 1

2 Select Insert from the main menu Plotting in Excel Select All Chart Types San Jose State University Engineering 10 2

3 Definition: A chart that consists of multiple columns (vertical bars), and the height of each column represents the quantity associated with the corresponding category. Use this type of chart for visual comparison of the quantities associated with different categories Column Chart San Jose State University Engineering 10 3

4 Column Chart - Example Select Insert Column Chart 2D Column Category No. of Student Frosh 4000 Sophomore 3500 Junior 6800 Senior 7000 Graduate 8000 Select data range San Jose State University Engineering 10 4

5 Column Chart - Example Chart Layout options Select the option with Chart Title and Axes Title San Jose State University Engineering 10 5

6 Edit the chart and axes titles, place the curser on the text and right click Column Chart - Example A plot must have a title and a description of the axes, including units if applicable San Jose State University Engineering 10 6

7 Grade Multi-Column Chart - Example Frosh Sophomore Junior Senior Grad Multiple Column Charts are used for Comparison, select all three columns. Include title, description for axes and modify the legends. San Jose State University Engineering 10 7

8 Pie Chart Definition: A graph in the shape of a circle divided into sectors, whose areas correspond to the proportions of the quantities. Application: Visual representation of relative magnitudes of a given set of quantities San Jose State University Engineering 10 8

9 Pie Chart Use Chart Layout Label the Chart San Jose State University Engineering 10 9

10 XY plots are two dimensional graphs. Scientifically, it is a plot of independent variable (x) against a dependent variable (y). The plot is used to obtain a functional relationship between two variables There are five options in Chart sub-type menu. The first option, where only points are plotted, is the most common type used in engineering and science fields. A curve is fitted to the plotted points to obtain the function describing the relationship between the two variable. XY (Scatter) Plots San Jose State University Engineering 10 10

11 XY (Scatter) Plots - Example Select Chart Layout (Layout 1) San Jose State University Engineering 10 11

12 Fitting a Curve to Data Points (XY) Given the plot of test results, the question is what would be your test score if you studied for 2.5 hours, no data is available for 2.5 hours. In order to answer the question, you have to find the equation relating the test score to the number of hours spent studying. San Jose State University Engineering 10 12

13 Fitting a Curve to Data Points (XY) Engineers frequently collect paired data in order to understand the characteristics or behavior of an object or a system. The goal is to capture the overall trend reflected by the entire data set. This can be achieved by obtaining the equation of a curve (or a straight line) that best describes (fits) the data points. The Method of Least Squares is used for this purpose. The Method of Least Squares minimizes the sum of the squares of the errors. San Jose State University Engineering 10 13

14 Fitting a Curve to Data Points (XY) The Method of Least Squares can be used to fit many different types of functions through a set of data points. The data obtained in many engineering applications may be represented by a straight line, exponential function, a power function, or a polynomial. Equation Type Linear (straight line) Mathematical expression y = ax + b Exponential Power y = ae bx y = ax b Logarithmic y = a ln(x) + b Polynomial (up to 6 th order) y = c 1 + c 2x + c 3 x c k +1x k In Excel k = 6 The Method of Least Squares obtains the appropriate set of values for the coefficients, a, b, c 1,. San Jose State University Engineering 10 14

15 Fitting a Curve to Data Points (XY) Data point Select a data point and right click, then choose Add Trendline option. Select the curve to fit the data. Check the Set Intercept box to force the curve to pass through origin (0,0). Check the Display Equation on chart and the Display R-squared value on chart boxes. San Jose State University Engineering 10 15

16 Fitting the best Curve to Data Points There are six option to select from, start with your best guess and check the fit. The best fit is indicated by how close the correlation factor, R 2, is to unity, the closer to 1 the better the fit. Linear Exponential Polynomial (3 rd order) Polynomial (5 th order) San Jose State University Engineering 10 16

17 Fitting the best Curve to Data Points Given the plot of test results, the question is what would be your test score if you studied for 2.5 hours, no data is available for 2.5 hours. Substitute x = 2.5 in the 5 th order polynomial equation to find y (hours spent studying). y =.2361(2.5) (2.5) (2.5) (2.5) (2.5) 60 y = (exam score for 2.5 hours of studying) Equation Type Exponential R-squared value.675 Exam Score 62.9 Linear.73 Best answer 65.5 Polynomial (3 rd order) Polynomial (5 th order) Best fit (does not make sense) San Jose State University Engineering 10 17

18 Histogram There are times that is desirable to plot the data in a manner that shows how the values are distributed within a certain range. This type of plot is called a histogram (a relative frequency plot). An engineer is responsible for monitoring the quality of 1000-ohm resistors. To do this, the engineer must measure the resistance of a number of resistors within a batch selected at random. The results are shown below. The acceptable variation is ± 2% ( ). The question is how many resistors fall within the acceptable range. Sample No. Resistance, ohm Sample No. Resistance, ohm Use the Max and MIN functions to find: Smallest value = 935 Largest value = 1045 San Jose State University Engineering 10 18

19 Data menu Histogram If Data Analysis (or Solver) does not appear, select File and choose Options, select Add-Ins, click on Go and check the boxes for Analysis ToolPak and Solver San Jose State University Engineering 10 19

20 Histogram To create a histogram, you must first subdivide the range of the data into equally spaced intervals. The first interval must start at or below the smallest data value, and the last interval must extend to or beyond the largest data value. The interval bounds is called the Bin Range in Excel. Smallest value = 935 Largest value = 1045 The acceptable variation is ± 2% (980 to1020). Create the Bin range Find the desired interval: 40 ( =40) The Bin Range Create a column in the Excel for the Bin Range 900 < > 1045 San Jose State University Engineering 10 20

21 Histogram Data range (has to be in one column) Bin range Select Data Analysis and choose Histogram Select to obtain a histogram plot San Jose State University Engineering 10 21

22 Histogram 16 data values fall in the range San Jose State University Engineering 10 22

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