lecture 2: formulas & functions
TRANSCRIPT
MTH4114: Computing and Data Analysis with Excel
Lecture 2: Formulas & Functions
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Labs
Labs are
• Thursday 9-11 (Online and On Campus)
• Friday 12-2 (On Campus only)
• Friday 2-4 (On Campus only)
Please come to your assigned lab!!
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Labs (prep work)
Preparation needed for Labs
• Review the lecture content
• Read the exercises
• You do not need to do the exercises before the lab (unlike your other modules)
Before the Labs this week:
• Make sure you can access Excel: either your own copy or appsanywhere
• Make sure you know which lab you are assigned to.
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AutoFill (end of Lecture 1)
AutoFill can automatically complete ‘sequences’ of data, e.g. to enter the first 40 days of the year into cells A1 to A40, you can just
• Type 01-Jan into cell A1 and 02-Jan into cell A2
• Use the mouse to select A1 and A2 together
• Drag the cursor from the bottom-right corner of A2 to A40
• Excel will try to guess what you mean when you try to use AutoFill, and after you have done the AutoFill you can use the AutoFill icon to select options
• AutoFill can also copy formulas: (but copy and paste is just as good in this case)
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Reminder: Entering formulas
Last week, we started to discuss formulas
Remember all formulas start with an equals sign =
There are several ways to enter a formula into a cell:
• Type the formula into the cell directly
• Select the cell and then type the formula into the formula bar
• Select the cell and then use the formula builder by clicking . This tool is also called the “Insert Function” tool.
• Click on the Formulas tab and use the various shortcuts
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Reminder: formulas
Examples:
• Mathematical functions, e.g. =SIN(0) (sine of 0), =COS(1) (cosine of 1), =LN(3) (natural logarithm of 3), etc.
• Functions on ranges: SUM, AVERAGE etc
This week, we
• Look at the formula builder in more detail, and
• discuss some important functions.
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Some examples
Sum: Average:
We see the basic syntax:
=FUNCTION(Arguments)
• '=' identifies the input as a function to be evaluated
• FUNCTION is the name of the function (above: SUM & AVERAGE)
• Arguments are the inputs to the function (above the values to be added / averaged)
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'=' identifies the command as a function:
Basic Syntax: function
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Incorrect:Without the = the input is identified as text
Correct:The formula is identified and evaluated
Basic Syntax: Arguments
Arguments are the input to a function, just like for mathematical functions
Arguments may be
• A reference to a single cell (e.g. A1)
• A reference to a range of cells (e.g. A1:A6)
• A manual input. E.g. numbers such as 1.5, or text (which needs to be in quotes "Pass")
• The output of another function. That is you may nest functions. E.g., =SIN(COS(1))
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Basic Syntax: Arguments
• Multiple inputs, separated by a comma, can be given for some functions. For example
• '=SUM(3, 6, -7)' which will give 2
• '=SUM(A1:A6, 6)' will sum the values A1 to A6 and then add 6
• With multiple inputs, we can mix the different types:
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Basic Syntax: Errors
The behaviour for different types of arguments depends on the function
• #VALUE! is displayed, when the arguments don’t match the function (or a warning pops up)
• E.g. if a function expects a number but the argument is text.
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Basic Syntax: Errors
• If your formulas contain circular references (e.g. if you enter =D10 in cell D9 and =D9 in cell D10) you will see a warning like this one at the bottom of the screen:
You may also see an error box like the one below.
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Required Arguments
• Most functions have at least one required argument. The function cannot be calledwithout these arguments.E.g. calling '=SUM()':
• Some functions require two or morearguments. E.g., '=LEFT(text, number_of_characters)'
• A very small number of functions do not require an argument: they do still require empty parenthesis:E.g. '=PI()' which returns the value of 𝜋.
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Optional Arguments
Some functions have additional optional arguments. These arguments are not necessary but are used when provided
• Example: SUM(number1, number2, …)
• One input 'number1' is required, the remaining input numbers are optional. Note 'number' can be a single number or a range.
• '=SUM(A1:A6)' sums the values in the six cells A1 to A6
• '=SUM(A1:A6, C1:C6, E1:E6)' sums the values in the 18 provided cells
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Finding functions
How do you find Excel functions?
• ‘Formulas’ tab
• ‘Insert function’ tool
• We focus on the Excel tools, but Google (and stackoverflow.com) is always a good place to search for answers related to computing questions
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Insert Function tool
Insert Function tool
• Displays all functions available
• Grouped by most recently used, or by category
To insert a function:
• Click left of the formulabar
• Find a function and read description for its usage
• Click 'OK' to add function
• Insert arguments and pressenter to evaluate function
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Function dialog box
Function Arguments dialog box
• Helps you enter all of thecorrect values as functionarguments
• Each argument is listed,required ones are in bold
• Help info displayed for current argument text box
• Preview of data at right
• Results are instantly calculated and displayed if enough arguments entered
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Function dialog box
• Function arguments dialog box shrinks temporarily using collapse button. This is useful if you want to select a cell or range with the mouse.
• Restores to full size when done
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Formulas Tab
The ‘Formulas’ tab is a shortcut to functions grouped by their category:
Categories:
• Financial: Specialised financial computations, such as IRR (internal rate of return), duration (of a bond), FV (future value of an investment)
• Logical: Conditional statements, where a different formula can be used when a condition is fulfilled
• Text: Manipulate text strings and convert numbers to text (and vice versa)
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Formulas Tab
Categories:
• Date & Time: Create and manipulate date and time values. E.g. get today's date with TODAY() or get date and time with NOW()
• Lookup & Reference: Find data entries in the spreadsheet or link to online resources
• Maths & Trig: Find standard mathematical functions, such as logarithms, cosines and rounding
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More functions
Further categories (found under “More Functions”)
• Statistical: Stochastic functions:
• empirical investigations, e.g. computing sample means and sample standard deviations;
• probability theory, e.g. evaluating the normal distribution.
• Engineering: Some mathematical tools for engineers
• Cube: Database connection
• Information: Get information about data in another cell, e.g. is it a number?
• Compatibility: Functions from former Excel versions that were replaced and are only available to allow old files to be opened.Deprecated: Do not use, unless you have a valid reason to do so
• Web: Specialised functions to work with URLs and webservices.
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Standard Mathematical Functions
Most mathematical functions can be called as intuitively expected:
• LOG(num, base) computes the logarithm of num to the specified base (default base of 10 is used if omitted)
• LN(num) computes the natural logarithm of num (i.e. to the base of e)
• EXP(num) computes the exponential function (i.e. e to the power of num)
• SIN(num) computes the sine of an angle (given in radians)
• ABS(num) computes the absolute value of num.
• SIGN(num) returns the sign of a value (i.e. 1 for positive, -1 for negative values and 0 for 0)
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Sum functions
Excel has several functions for doing summation:
• SUM: Adds all the numbers in a range of cells'=SUM(A1:A6)' returns 21 (1+2+3+4+5+6)
• SUMSQ: Adds all the squares of the numbers ina range of cells.'=SUMSQ(A1:A6)' returns 91 (12 +…+62)
• SUMPRODUCT: Adds the product of corresponding entries of arrays:'=SUMPRODUCT(A1:A6, B1:B6)' returns 56 (1*6 + 2*5 + … + 6*1)
• SUMX2MY2: Sums the differences of the squares of corresponding entries of arrays:'=SUMX2MY2(A1:A6, B1:B6)' returns 0
(12−62)+(22−52)+…+(62−12)
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Auxiliary Cells
• On the previous slide we saw some examples of “complicated” summation formulas like SUMPRODUCT.
• A different way to do this is:
• Enter the formula =A1*B1 in cell C1.
• Copy that formula into cells C2:C6[At this point each cell in column C is the product of the two elements in columns A and B.]
• Now put =SUM(C1:C6) into cell C7.
• The value in C7 is exactly theSUMPRODUCT(A1:A6,B1:B6)
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Example setup:
Auxiliary Cells: Pros and Cons
Advantages
• Easier to remember
• Easier to understand
• Easy to check the formulas are doing what you expect.
Disadvantages
• Less “clean” – the spreadsheet is more cluttered. (Can be mitigated by hiding the column)
• May not “fit” neatly if you want to do lots of processing after the complicated sum.
Summary
As a guide use auxiliary cells if the spreadsheet’s purpose is to calculate things, and use the fancier formulas if the purpose is to communicate things.
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Nesting of functions
Mathematical functions are often nested: the output of a function is the input to another one
• Example: Computing the Euclidian norm (length) of a vector (x,y,z), so length is √(𝑥2+𝑦 2 +𝑧 2), is a composition of SUMSQ and SQRT:
• First SUMSQ computesthe sum of squares𝑥^2+𝑦^2+𝑧^2, which is directly passed on to SQRT to compute the square root.
• Alternatively you could use the formula '=SQRT(A2^2+B2^2+C2^2)' if you preferred.
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Dates
As far as Excel is concerned a date is a number with some specific formatting.
• Therefore you can do “number” operations on dates
• Some of these make sense:
• =date_1 - date_2 gives the number of days between the dates.
• =date + 5 gives the date 5 days after ‘date’
• But others do not:
• =date_1 + date_2 is nonsense.
• It’s up to you to make sure what you are doing makes sense!
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Text functions
Excel has many functions for manipulating text:
• '=CONCAT(text_1,text_2)' returns text_1 followed by text_2
• '=LEFT(text, num_chars)' returns the specified number of characters from the start of ‘text’ (see also RIGHT and MID)
• '=SEARCH(text_1,text_2)' returns the position of the text text_1 inside text_2:
• E.g, =SEARCH("W","Mark Walters") returns 6
• E.g, =SEARCH(" ","Mark Walters") returns 5
See also FIND
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Text functions (examples)
• We can use CONCAT to join firstnames with surnames:
• You need the " " in the middleor you would get MarkWalters
• To go from full name to first name is more complicated but we can use a nested formula:
• '=LEFT(full_name,SEARCH(" ",full_name)-1)'
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Flash Fill
• We just saw how we could use formulas to join or split first and surnames.
• Flash-fill can often do things like this automatically. It does this by noticing patterns, e.g. if you have a list of forenames in column A and surnames in column B, you can easily create a list of full names in column C:
• Type the first full name in column C1
• Select column C2 and click the Flash-fill button in the Data tab
• WARNING! Excel is guessing! Make sure it guessed right.
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Flash Fill versus Formulas
Advantages of FlashFill:
• Easy!
• Easy!
Advantages of Formulas:
• You know exactly what it is doing.
• It will update if the source data changes:
• E.g. if you change someone’s surname the fullname automatically updates.
• There are lots of different ways to do things in Excel.
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CONDITIONAL FORMULAS
Sometimes you want Excel to do different things based on some data:
• E.g. Suppose you have a list of students in column E and their module marks in Column F. You want Column G to say whether they passed or failed.
• You can use the 'IF' function:=IF(F2>=40, "PASS", "FAIL")
• The IF function checks whether thecondition 'F2>=40' is met: if it is, it returns the second argument;if the condition is not true it returns the third argument.
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CONDITIONAL FORMULAS
Many Excel functions can be combined with IF as a single function: SUMIF, COUNTIF, AVERAGEIF
• The simplest of these is COUNTIF. The syntax is'=COUNTIF(range,criteria)' which counts the number of cells which meet the condition.
• =COUNTIF(F2:F6,">=40") gives 4
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CONDITIONAL FORMULAS
SUMIF and AVERAGEIF are similar but have an extra argument: the syntax is
• '=AVERAGEIF(range, criteria, average_range)' which averages the elements in average_range where the corresponding element in range meets the condition.
• Almost always range andaverage_range are a singlecolumn or row and thecondition is asking about data in the correspondingcolumn of the same row
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Absolute referencing
Last week we saw that usually Excel will 'translate' a formula if you copy and paste it. When would you not want this?
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Absolute referencing
In the example below some students have coursework marks for three courseworks out of 30, 15 and 55respectively. I want the percentage for each coursework. I entered the formula =B2/C$1 into C2 and the copied it to all of C2:C9, E2,E9 and G2:G9. You can see the formulain E5 is "correct"
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Absolute referencing
In the example below I have listed some flights and their cost excluding VAT. I have entered the VAT rate in cell F1.
By using absolute referencing in the formula '=(1+$F$1)*B2' in C2 I was able to copy it down the whole of column C.
Having the VAT rate in cell F1 means it is easy to update the sheet if the rate changes.
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