Shakeel Muzaffar

Convert fractions, decimals, and percentages fast: divide top by bottom, multiply by 100, or put over 100. See the six moves plus an equivalents table.

Ratios and proportions explained simply: a ratio compares amounts as a:b, a proportion sets two ratios equal. Learn to simplify, cross-multiply, and split a total.

Learn how to calculate percentage increase and decrease with new = old x (1 + p/100), reverse it to find the original, and see why +20% then -20% never cancels.

The percentage change formula is ((new – old) / old) x 100. See why you divide by the original value, what the sign means, and worked examples.

Learn how to calculate a percentage the easy way. Find X% of a number, work out what percent one number is of another, and use fast mental math tricks.

A five-number summary lists the minimum, Q1, median, Q3, and maximum. Learn to read spread, skew, and outliers from a box plot, with a worked example.

Percentiles and quartiles explained simply: a percentile is the percent of data at or below a value, and quartiles split sorted data into four equal parts.

A z-score tells you how many standard deviations a value is from the mean. Learn the formula z = (x – mean) / SD, a worked example, and the empirical rule.

Learn to calculate sample size with the formula n = z^2 * p * (1 – p) / e^2. A worked example gives n = 385 at 95% confidence and a 5% margin of error.

Standard deviation measures how spread out data is around the mean. See the formula in plain English, a full worked example, and population vs sample simply.