IEMJEE Maths preparation: Mean and population variance — practice worksheet with answers

How to use this worksheet

This independent worksheet checks mean and population variance with a new problem, an explanation task and an interleaved related skill. It is not an official IEM question paper, a difficulty forecast or a prescribed timed examination.

Write an attempt first, then compare your method with the visible answers. Record whether a miss came from interpretation, a missing concept, execution or a condition you overlooked.

Question 1: apply the topic

Find the population variance of 5,5,5.

Answer and checking point

Every deviation is zero, so the variance is zero.

Substitute a candidate result into the original statement where possible. Inspect sign, endpoint inclusion and whether a real or complex answer is requested. The simplified expression and the original expression can have different domains even when their nearby values agree.

Question 2: diagnose an approach

Explain why the following warning matters and identify the correction it calls for: Using n−1 without identifying a sample-variance estimator changes the requested quantity.

Model checkpoint: Variance measures squared spread around the mean. Population and sample denominators are different conventions. Governing rule: Population variance=(1/n)Σ(xᵢ−x̄)².

Question 3: transfer to union of two sets

Of 40 applicants, 22 study mathematics, 17 study computing and 8 study both. How many study neither?

Answer: The union is 22+17−8=31, so 40−31=9 study neither.

This is an interleaved related-skill task, not a claim that the two topics have identical methods. Explain which idea changes when switching from the main topic to this one.

Review the attempt

Separate correct answers reached with a justified method from lucky guesses. Rework missed steps without looking at the answer, then use a fresh problem from an appropriate primary textbook or official paper. Do not use a small worksheet result as an admission cutoff, rank or readiness guarantee.

Official sources and verification

Sources checked on 26 October 2026. A source’s date, programme and campus limit which claims it supports. Official pages may change after review.

1. UEM — IEMJEE examination information

   Historical examination pattern; verify the current cycle on the central portal.

2. NTA — explicitly labelled JEE Main 2026 syllabus

   Historical PCM syllabus reference. Lessons and exercises are independently authored, not official IEMJEE papers or verified 2027 paper predictions.

3. NCERT — official textbook catalogue

   Primary textbook reference for checking school-level concepts. This directory does not certify the independent lesson or establish IEM examination weightage.

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