Algebra & Numerical Reasoning

Averages

Calculating simple mean and weighted averages.

Applied in government payroll analysis, CPI reporting, and inventory accounting scenarios.

What the exam tests

Standard Simple Mean

Find the central value of a set of numbers by summing all items and dividing by the total count.

Weighted Average Scenarios

Different values are assigned different weights, which requires the weighted average formula rather than a simple mean.

Statistical Data Sets

Questions derived from results such as die rolls where you must identify the mean alongside median and mode.

Economic Index Problems

CPI calculations: the Consumer Price Index is defined as the weighted average of prices for a basket of goods and services.

Accounting Inventory Valuation

Weighted Average inventory method: calculate the value of shipped or remaining inventory using weighted costs per unit.

Formula Application

Key rules

  • Simple mean: X̄ = Σx ÷ n (sum of all items divided by the number of items).
  • Weighted average: X̄w = Σ(x × wᵢ) ÷ Σwᵢ (sum of each observation multiplied by its weight, divided by the sum of all weights).
  • Identify which formula applies: if all values count equally, use simple mean; if different values have different frequencies or importance, use weighted average.

Common traps

  • !Using simple mean when weights differ gives the wrong answer. Always check whether values have equal or unequal weights before choosing a formula.

Weight Identification and Data Filtering

Key rules

  • Distinguish between the primary observations (x) and their assigned weights (wᵢ) within a word problem or table.
  • Eliminate irrelevant information (names, dates, unrelated figures) before setting up the calculation.

Common traps

  • !In inventory problems, the 'weight' is the quantity of units purchased at each price, not the price itself.

Verification and Reasonableness

Key rules

  • A calculated average must fall between the lowest and highest values in the set. If it doesn't, recheck the arithmetic.
  • Substitute the answer back into the formula to verify the result.

Try one

An office manager tracks three supply orders totaling $237, $80, and $125. What is the simple mean (average) cost of these orders?

A.$147.33
B.$148.00
C.$221.00
D.$135.50

Sum = 237 + 80 + 125 = 442. Mean = 442 ÷ 3 ≈ $147.33.

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