Data Analysis Part 1: Excel, Log-log, & Semi-log plots

Transcription

1 Data Analysis Part 1: Excel, Log-log, & Semi-log plots

2 Why Excel is useful Excel is a powerful tool used across engineering fields. Organizing data Multiple types: date, text, numbers, currency, etc Sorting and filtering Performing calculations Copy-paste for repeated calculations Many functions available Results update automatically when input data changes Visualization Graphs (bar chart, scatter plot, pie chart, etc) Color-coding (conditional formatting) Create and copy charts to Word or PowerPoint 2

3 Entering values and formulas 3

4 Overview Tabs Save Copy/paste Change fonts and background Change cell type (number, date, etc) Add and delete rows or columns Formula bar Cells for entering data or formulas Multiple pages called sheets 4

5 Entering values and drag to complete Formula bar To enter a value: (1) Select a cell (2) Type the value directly in the cell or in the formula bar (3) Enter to finish or Esc to exit 5

6 Entering formulas into cells The equation (=A2*A2) appears in the cell and the formula bar. To enter a formula: (1) Select a cell (2) Type the formula (1) Start with an = Add: + Subtract: - Multiply: * Divide: / Power: ^ (2) Reference cells by typing the cell code (e.g. A2) or select the cell using your mouse (3) To edit part of the formula, use the formula bar above the cells (3) Enter to finish or Esc to exit 6

7 Copying formulas To copy a formula to other cells: (1) Select cell with formula (2) Crtl+c to copy (3) Select new cells (4) Ctrl+p to Paste or Click and drag the lower-right corner of a cell (shown here) 7

8 Using the $ symbol to maintain column and row references The equation for cell B9 is =A9*A9. Cell references in formulas are relative (e.g. the cell one column to the left). To prevent the column letter or row number from changing when you copy a formula, place a $ before the column letter and/or row number. 8

9 Graphing data 9

10 Types of charts in Excel NOTE: Use Scatter instead of Line plots when using trendlines. 10

11 Insert a scatter chart to graph the data Select the data you want to plot, then choose the plot type using the upper menu. Usually you will select a Scatter Plot. 11

12 Edit the chart using the + menu 12

13 Double-click the graph to get the right-hand menu 1. Double-click the chart to open the right-hand menu. 2. Use the drop-down menu (shown) to view different menu pages. 13

14 Add a trendline and show the equation on the graph Trendline options Select the function type Display equation 14

15 Excel functions 15

16 Using functions in formulas Enter the formula in the cell or the formula bar A formula can also include functions. See below for common functions Functions take arguments separated by commas Many arguments are cell names (e.g. A2) or cell ranges Click and drag to select a range of cells Common functions: AVERAGE( ) SUM( ) MAX( ) COUNT( ) PI( ) COS( ) LOG( ) SQRT( ) Cell range examples: A1:A20 Rows 1-20 in column A A1:D1 All cells in row 1 from column A to column D B10:D20 A block of cells in rows and columns B-D A1:A20,A1:D1,B10:D20 All previous ranges combined 16

17 Searching for Excel functions Type the cell range here OR click here to use the mouse to select the cells to SUM 17

18 Common functions in Excel AVERAGE( ): average of all cells in the range SUM( ): sum of all cells in the range MAX( ): maximum value for all cells in the range ABS( ): absolute value COUNT( ): counts the cells that contain numbers PI( ): returns the value of π COS( ): cosine for an input in radians LOG( ): logarithm (base 10) SQRT( ): square root STDEV( ): standard deviation 18

19 Semi-log and log-log plots 19

20 Line of best fit Engineers deal with several types of functions. A small subset includes: Type General equation Example Linear y = mx + b y = 3x + 5 Power-law y = Ax n A = πr 2 Exponential y = An cx c = 10(2) t/10 Quadratic y = Ax 2 + Bx + C y = 3x 2 + 4x + 5 What happens when you have data but don t know the equation? Plot the data and add a trendline, also known as a line of best fit Trendlines can be linear, exponential, etc (we focus on linear in EI) Excel can calculate trendlines All images are in the public domain. 20

21 Log-log plot for area of a circle Area of a circle: Area for a circle Take the log of both sides log a xy = log a x + log a y log a x n = nlog a (x) A = πr 2 log 10 A = log 10 πr 2 log 10 A = log 10 π + log 10 r 2 log 10 A = log 10 π + 2log 10 (r) If we plot log A vs log r, what should we expect? We expect a straight line with a slope of 2 and an intercept of log π 21

22 Quiz Use Excel to create a log-log plot with trendline for the volume of a sphere vs radius: LOG(volume) vs LOG(radius). Radius (m) Volume (m^3)

23 Semi-log plot for colony of bacteria Number of bacteria in a colony that doubles in size every 10 minutes Count (C) based on minutes (m) C = C 0 2 m/10 Take the log of both sides log 2 C = log 2 C 0 2 m/10 log a xy = log a x + log a y log 2 C = log 2 C 0 + log 2 2 m/10 log a x n log a a = 1 = nlog a (x) log a b = log c(b) log c (a) Multiply by log 10 (2) log 2 C = log 2 C 0 + m/10 log 2 (2) log 2 C = log 2 C 0 + m/10 log 10 (C) log 10 (2) = log 10(C 0 ) log 10 (2) + m/10 log 10 (C) = log 10 (C 0 ) + m/10 log 10 (2) If we plot log C vs m, what should we expect? 23

24 Quiz Use Excel to create a semi-log plot with trendline for the bacteria growth: LOG(bacteria count) vs minutes. Start with 10 bacteria at time = 0 minutes. Min Count x 24

25 Quiz 1. How would you determine if the relationship between two variables was Linear, Power-law, or Exponential? Plot y vs x Plot LOG(y) vs LOG(x) Plot LOG(y) vs x 2. If you plot LOG 10 (y) vs LOG 10 (x) and find a straight line with slope 5 and an intercept of 2, what is the equation relating x and y? [log-log plot] y = Ax n log b y = n log b x + log b (A) y = 100x 5 slope = n intercept = log b (A) A = b intercept 3. If you plot LOG 10 (y) vs x and find a straight line with slope 3 and an intercept of 1, what is an equation relating x and y? [semi-log plot] y = An cx slope = log b n c log b y = log b n cx + log b (A) intercept = log b (A) y = 10(10) 3x NOTE: We can choose n or c. 25