Four Quantitative Errors Repeated by Students in Qiyas Tests and How to Avoid Them

Percentage Errors: Increase and Decrease

Students err when reading "the price increased by 20%" and multiply the original value by 0.20 only, forgetting to add it to the original. The reverse occurs with decrease: subtracting from the original without calculating the new value. A common example: a shirt priced at 100 riyals increases by 20% then decreases by 20%. The hasty student assumes the price returns to the original, while the correct answer is 96 riyals.

How to avoid: Always write the equation: New Value = Original × (100% ± Percentage). With successive decreases, never add percentages; calculate each step separately.

Confusing the Mean with the Median

The arithmetic mean is calculated by summing values and dividing by their count. The median is the middle value after ordering. The error occurs when a question asks for "the most common number" or "the value exceeded by half the data" and the student answers with the mean. Example: scores of five students are 60, 70, 80, 90, 100. The mean is 80, and the median is also 80. But add an outlier of 10, the mean becomes 68.3 and the median becomes 70, and this difference changes the correct answer.

How to avoid: Verify the question's wording. "Mean" or "average" indicates the arithmetic mean. "Median" or "middle value" indicates ordering and finding the center. If it says "most frequent value," the mode is required, not either of these.

Misreading Graphs

Three errors repeat: reading the vertical axis from zero instead of the starting value, confusing a column with its adjacent category, and hastily comparing lengths without checking the scale. Example: a graph whose axis starts at 50 rather than zero makes the difference between 60 and 70 appear visually large when it is only 16% in reality.

How to avoid: Before any calculation, answer three questions: What is the zero point? What is the unit of measurement? What is the true numerical difference between the two values being compared?

Unit Conversion Errors

Multiplying instead of dividing, or vice versa, or forgetting squaring and cubing for areas and volumes. Example: converting 2 square meters to square centimeters. The error: multiplying by 100 to get 200. The correct: multiplying by 10,000 because the conversion concerns area, not length.

How to avoid: Write the conversion chain step by step. Meter = 100 cm, therefore square meter = 100 × 100 cm². Remember the exponent rules: conversion in n dimensions means exponent n for the factor.

Conclusion: This Week's Practice

Allocate fifteen minutes daily to four questions: one on successive percentages, one asking for the median from data with outliers, one requiring reading of a deceptive graph, and one on cubic unit conversion. Verify your answer by rewriting, not by visual estimation. This systematic verification reduces errors before increasing speed.