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Statistics: Mean, Median and Mode Practice Questions with Detailed Solutions – Level 2

Medium-level statistics practice on combined and corrected means, median from frequency tables, missing frequencies, the empirical relation, coefficient of range and standard deviation.

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Questions, answer key and solutions.

Questions
50
Duration
60 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 60-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. 60 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

Statistics Level 2 Practice: Mean, Median, Mode and Frequency-Table Questions

Students who are comfortable with basic averages and want medium-level practice will find this Level 2 Aptitude360 set useful. It covers mean, median and mode in harder settings: combined means, frequency tables with a missing value, the empirical relation with decimals, coefficient of range, and variance and standard deviation. Worked solutions are given for every question.

What the Level 2 mean, median and mode questions test

  • Replacing, removing or adding observations and finding the changed mean
  • Correcting a mean after more than one value was copied wrongly
  • Combined mean of two groups and the required score for a target average
  • Median of unsorted data and median from a discrete frequency table
  • Finding a missing frequency or an unknown value from a given mean or median
  • Empirical relation between mean, median and mode, including differences between them
  • Coefficient of range, variance, standard deviation and sum of squares from mean and variance
  • Linear transformation of data, including multipliers less than zero

Important formulas and rules for Level 2

  • Combined mean: \( \dfrac{n_{1}\bar{x}_{1}+n_{2}\bar{x}_{2}}{n_{1}+n_{2}} \)
  • Coefficient of range: \( \dfrac{L-S}{L+S} \)
  • Variance shortcut: \( \sigma^{2}=\dfrac{\sum x^{2}}{n}-\bar{x}^{2} \)
  • Mean minus mode: \( \bar{x}-\text{Mode}=3(\bar{x}-\text{Median}) \)
  • If \( y=ax+b \): \( \sigma_{y}^{2}=a^{2}\sigma_{x}^{2} \)

How to prepare for medium-level statistics problems

  • Rearrange the variance shortcut to get the sum of squares when mean and variance are given.
  • In a frequency table, build cumulative frequencies before locating the median.
  • For a missing frequency, write the mean equation with the unknown in both the numerator and the total frequency.
  • Under a linear change, the new mean is the multiplier times the old mean plus the added constant, while the standard deviation is multiplied by the absolute value of the multiplier.

Who this Level 2 set suits

It suits aptitude aspirants who have finished the basic level and want stronger practice before moving to the hardest statistics problems.

FAQs about Statistics: Mean, Median and Mode Practice Questions with Detailed Solutions – Level 2

How do you find a missing frequency when the mean is given?
Write the mean as the sum of frequency times value divided by the total frequency, keeping the unknown frequency in both parts. Equate this to the given mean and solve the linear equation.
What is the coefficient of range in statistics?
It is the difference between the largest and smallest values divided by their sum. Being a ratio, it lets you compare the spread of data sets measured on different scales.
How do you find the median from a frequency table?
Form the cumulative frequency column and locate the middle position of the ordered data. If the total frequency is odd, the value at that single middle position is the median; if it is even, locate both middle observations and average their values.
What is the relation between variance and standard deviation?
Standard deviation is the positive square root of the variance. Variance is the mean of the squared deviations from the mean.

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 25060 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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