)` -> corrected: `=IF(B2>=75,

Instructional Goals and Core Operating Principle

• Excel performs automated computations, but the accuracy of every result depends entirely on correct formula construction.
• Core learning objectives:
  • Explain how Excel systematically applies the order of operations when evaluating formulas.
  • Construct functional formulas utilizing standard arithmetic operators alongside cell references.
  • Apply core Excel functions, specifically SUM, AVERAGE, MIN, MAX, COUNT, and IF.
  • Analyze real-world scenarios to select and execute the correct formula or function.

Foundations of Excel Formulas and Arithmetic Operators

• Formula definition:
  • A formula is an explicit calculation entered directly into a worksheet cell.
  • Syntactic mandate: Every formula must begin with an equal sign (=).
  • Function of cell references: Formulas link dynamically to coordinates of other cells rather than relying solely on static numbers.
  • Concrete calculation example: In the formula =B2+C2, if cell $B2$ contains $12$ and cell $C2$ contains $8$, Excel calculates $12 + 8 = 20$ and returns a result of $20$.
• Standard arithmetic operators in Excel:
  • Addition (+): Computes the sum of terms (e.g., =A1+B1).
  • Subtraction (-): Computes the difference between terms (e.g., =A1-B1).
  • Multiplication (*): Computes the product of terms using the asterisk symbol (e.g., =A1*B1).
  • Division (/): Computes the quotient using the forward slash symbol (e.g., =A1/B1).
  • Exponentiation (^): Raises a base to an exponent using the caret symbol (e.g., =A1^B1).

Excel's Order of Operations (PEMDAS)

• Evaluation hierarchy:
  • Excel processes mathematical operations within formulas strictly according to algebraic precedence, summarized by the mnemonic PEMDAS:
  • Priority 1: Parentheses () — Expressions enclosed within parentheses are evaluated first.
  • Priority 2: Exponents ^ — Powers and exponential terms are evaluated second.
  • Priority 3: Multiplication and Division (* and /) — Evaluated third.
  • Priority 4: Addition and Subtraction (+ and -) — Evaluated fourth.
• Directional tie-breaking rules:
  • Multiplication and division share equal priority; when both appear in a formula, Excel evaluates them sequentially from left to right.
  • Addition and subtraction share equal priority; when both appear in a formula, Excel evaluates them sequentially from left to right.

Worked Calculations: Operation Precedence vs. Grouping

• Unparenthesized formula evaluation:
  • Given formula: = 6 + 2 * 5
  • Step 1 (Multiplication precedes addition): Excel identifies multiplication as having higher priority than addition and computes $2 \times 5 = 10$.
  • Step 2 (Addition execution): Excel adds the remaining term to the product: $6 + 10 = 16$.
  • Final displayed result: $16$.
• Parenthesized formula evaluation (overriding default order):
  • Given formula: =(6 + 2) * 5
  • Step 1 (Parentheses evaluated first): Excel calculates the terms inside the parentheses: $6 + 2 = 8$.
  • Step 2 (Multiplication execution): Excel multiplies the evaluated sum by the outside factor: $8 \times 5 = 40$.
  • Evaluation progression: =(6+2)*5 $\rightarrow$ 8*5 $\rightarrow$ $40$.
  • Operational rule: Parentheses alter the natural calculation order. They must be used whenever a specific group of operations must resolve prior to default arithmetic evaluation.

Anatomy and Structure of Excel Functions

• Definition:
  • A function is a pre-programmed, ready-made formula built directly into Excel to streamline repetitive calculations.
• Raw formula vs. built-in function:
  • Manual formula approach: =B2+B3+B4+B5 requires writing out every individual cell reference and operator.
  • Function approach: =SUM(B2:B5) consolidates the operation into a single command over a specified range.
• Universal function syntax:
  • Standard structure: =FUNCTION_NAME(argument)
  • Leading equal sign (=): Informs Excel that the entry is a dynamic formula.
  • Function name: The uppercase predefined routine identifier (e.g., SUM, AVERAGE).
  • Argument: Cell references, ranges, or values placed within parentheses (...) upon which the function acts.
• Range notation and the colon (:) operator:
  • The colon operator signifies the word "through."
  • For example, the range reference B2:B5 includes cells B2, B3, B4, and B5.

Core Built-In Functions: Aggregation and Statistics

• SUM:
  • Formula syntax: =SUM(B2:B6)
  • Functionality: Adds all numerical values contained within the specified range B2:B6.
• AVERAGE:
  • Formula syntax: =AVERAGE(B2:B6)
  • Functionality: Calculates the statistical mean of the numerical values across B2:B6.
• MIN:
  • Formula syntax: =MIN(B2:B6)
  • Functionality: Identifies and returns the smallest numerical value (minimum) within B2:B6.
• MAX:
  • Formula syntax: =MAX(B2:B6)
  • Functionality: Identifies and returns the largest numerical value (maximum) within B2:B6.
• COUNT:
  • Formula syntax: =COUNT(B2:B6)
  • Functionality: Tallies only the cells containing numbers within the designated range B2:B6.
• COUNTA:
  • Formula syntax: =COUNTA(A2:A6)
  • Functionality: Tallies all non-empty cells within the range A2:A6, counting cells containing text, numbers, or boolean values.

Logical Operations: The IF Function

• Operational role:
  • The IF function evaluates a specified condition and returns one outcome if the condition is TRUE, and an alternative outcome if it is FALSE.
• Structural syntax:
  • Standard format: =IF(condition, "value if true", "value if false")
  • The condition represents a logical comparison (such as >=, <=, >, <, =, <>).
  • The true and false values define the outputs returned based on the conditional test.
• Practical academic grading example:
  • Rule: A learner passes an assessment if their score is $75$ or higher.
  • Formula entered into cell C2: `=IF(B2>=75,