Statistics - How It Appears in JEE

8 recurring patterns. Learn the pattern, recognize it in 5 seconds, apply the right approach.

Find Mean / Median / Mode

Pattern

Compute central tendency measures from given data

How to recognize

Problem gives raw data or frequency table and asks for mean, median, or mode

→ For mean: use direct or shortcut method. For median: arrange data, find N/2, locate median class. For mode: find class with highest frequency.

Find Variance / Standard Deviation

Pattern

Calculate spread of data using variance or SD formulas

How to recognize

Asks for variance, SD, or spread of a data set. May give partial sums like sum of xᵢ and sum of xᵢ².

→ Use shortcut formula: Var = (sum of xᵢ²)/n - (mean)². Take square root for SD. Check if grouped or ungrouped.

Effect of Adding / Multiplying a Constant

Pattern

How does adding or multiplying a constant affect mean, variance, and SD?

How to recognize

Phrases like 'each observation is increased by k', 'multiplied by c', 'if 5 is added to each value'

→ Adding constant k: new mean = old mean + k, variance unchanged. Multiplying by c: new mean = c times old mean, new variance = c² times old variance.

Combined Statistics

Pattern

Find mean or variance of combined groups from individual group statistics

How to recognize

Two or more groups with given means, SDs, and sizes. Asks for combined mean or combined variance.

→ Combined mean = weighted average of means. Combined variance uses the formula with dᵢ = group mean - combined mean.

Frequency Distribution Problems

Pattern

Problems involving grouped frequency data with class intervals

How to recognize

Data given in class intervals with frequencies. May ask for mean, median, mode, or SD of grouped data.

→ Use class marks (midpoints) as xᵢ. Apply the grouped data formulas. For median, build cumulative frequency table.

Correction of Data / Missing Value

Pattern

One observation was wrongly recorded, or a value is missing. Find the corrected statistic.

How to recognize

Phrases like 'one value was wrongly taken as', 'a value was misread', 'if the correct value is'

→ Corrected sum = old sum - wrong value + correct value. Corrected sum of squares = old sum of squares - (wrong)² + (correct)². Recompute mean and variance.

Data Interpretation

Pattern

Interpret given statistical data to answer questions about central tendency or spread

How to recognize

Given mean deviation, coefficient of variation, or asks to compare two data sets using statistical measures

→ Mean deviation = average of absolute deviations. Coefficient of variation = (SD/mean) x 100. Lower CV means more consistent data.

Variance with Algebraic Constraints

Pattern

Find variance when observations satisfy algebraic conditions

How to recognize

Given sum of xᵢ, sum of xᵢ², or the observations are in AP/GP. May involve unknowns.

→ Use Var = (sum of xᵢ²)/n - (sum of xᵢ/n)². Plug in the given sums. For AP, use properties of arithmetic progressions.

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