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Statistics: Mean, Median and Mode Practice Questions with Detailed Solutions – Level 3

Advanced statistics problems on grouped mean and mode, corrected averages, missing frequencies, rescaled scores, coefficient of variation and standard deviation, each solved step by step.

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Questions, answer key and solutions.

Questions
50
Duration
75 min
Marks
50

Negative marking

Attempts
100
Access
Free
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Normal practice, or a Simulated test

Both use the same questions. Normal practice is untimed and needs no account: choose an option and the answer and solution appear at once. The Simulated test is the real computer-based format, with one 75-minute clock, a question palette and full screen, and your score, the key and the solutions arrive when you submit.

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Every question on one page, loading as you scroll. Choose an option and see straight away whether it was right.

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  • Solutions in place. The explanation, and the video where one has been added, sit under the question.
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Simulated

Timed CBT

The computer-based test format: one clock, a question palette, and a score the moment you submit.

  • A clock that does not pause. 75 minutes from the moment you begin, and the paper is submitted for you when it reaches zero.
  • Question palette. Answered, not answered and marked for review, section by section, as the real interface has it.
  • Full screen, proctored. The test takes over the screen; leaving it three times submits the paper.
  • Answers hidden until you submit. The key, the explanations and your score all arrive together at the end.

About this test

Mean, Median and Mode Level 3: Hard Statistics Problems with Solutions

Grouped-data mean and mode, rescaled scores, coefficient of variation and multi-step corrections to averages form the core of this Level 3 statistics set. It is the advanced Aptitude360 practice quiz on mean, median and mode, where most questions need two or more steps and some combine several measures. Each question has a worked solution.

Topics in this advanced mean, median and mode set

  • Corrected mean after several wrong entries and averages after members join or leave
  • Mean of class-interval data using class midpoints, and missing frequencies with a known total
  • Mode of grouped data using the modal class formula
  • Median after observations are added or struck off
  • Using mean, median and mode together with unknowns in the data
  • Variance, standard deviation, and recovering missing observations from mean and variance
  • Rescaling test scores linearly and finding the coefficient of variation of a transformed variable
  • Range of combined sets and extreme values under mean and median constraints

Advanced formulas for statistics problems

  • Grouped mode: \( l+\dfrac{f_{1}-f_{0}}{2f_{1}-f_{0}-f_{2}}\times h \)
  • Grouped mean: \( \bar{x}=\dfrac{\sum f_{i}m_{i}}{\sum f_{i}} \)
  • Coefficient of variation: \( \dfrac{\sigma}{\bar{x}}\times 100 \)
  • Sum of squares: \( \sum x^{2}=n(\sigma^{2}+\bar{x}^{2}) \)
  • Squares of first \( n \) naturals: \( \dfrac{n(n+1)(2n+1)}{6} \)

Revision tips for hard statistics questions

  • Track the total sum through every change, since most average problems reduce to fixing the total.
  • For grouped mode, identify the modal class by highest frequency and read the neighbouring frequencies carefully.
  • Adding an observation equal to the mean keeps the mean fixed and lowers the variance whenever the original variance is positive, so recompute using the sum of squares.
  • To maximise one value under a mean and median condition, keep the other values as small as the conditions allow.

Who should take Level 3

Aspirants who have completed the earlier levels and want tough, multi-step statistics practice for quantitative aptitude should take this set.

FAQs about Statistics: Mean, Median and Mode Practice Questions with Detailed Solutions – Level 3

How do you find the mode of grouped data?
Locate the modal class, the class with the highest frequency. Mode equals its lower limit plus class width times the difference between the modal and preceding frequencies, divided by twice the modal frequency minus the preceding and succeeding frequencies.
How is the mean of grouped data calculated?
Take the midpoint of each class, multiply each midpoint by its frequency, add these products and divide by the total frequency.
What is the coefficient of variation?
It is the standard deviation divided by the mean, multiplied by hundred, and is expressed as a percentage. When comparing data sets with positive, nonzero means, a lower coefficient of variation indicates more consistent data.
How do mean and standard deviation change when data is multiplied by a constant and a constant is added?
The new mean equals the multiplier times the old mean plus the added constant. The new standard deviation equals the absolute value of the multiplier times the old standard deviation, and the added constant has no effect on it.

Test structure

How the paper is split, and how long each part runs. A section you have finished cannot be returned to.

SectionQuestionsTime
Statistics: Mean, Median and Mode Level 35075 min

Marking & rules

Total marks
50 across 50 questions.
Negative marking
A wrong answer costs marks. Leaving a question unanswered costs nothing.
Attempts
100 in total. An attempt is spent the moment you begin one.

What you get when you submit

The analysis is ready the moment you submit the paper.

Score and accuracy

Marks, percentage, right, wrong and skipped, and the time you took.

Section by section

The same figures for each section, so a weak one cannot hide in an average.

The full answer key

Every question with your answer, the right one, the working, and the video where there is one.

Where you stand

Your score against the spread of everyone else who has sat this test.

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