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Statistics: Mean, Median and Mode Practice Questions with Detailed Solutions – Level 1

Easy statistics practice on mean, median, mode and range, correcting a wrongly recorded value, the empirical relation and how scaling data changes variance and standard deviation.

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Questions, answer key and solutions.

Questions
50
Duration
50 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 50-minute clock, a question palette and full screen, and your score, the key and the solutions arrive when you submit.

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How the two modes differ
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Normal

Untimed

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

  • No timer. Nothing to start and nothing to submit. Stop whenever you like.
  • Answered as you choose. Tap an option and it is marked at once, with the correct answer shown.
  • Solutions in place. The explanation, and the video where one has been added, sit under the question.
  • Open to guests. Normal practice needs no sign-in.
Real exam conditions

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. 50 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 1 Practice Quiz: Basic Statistics Questions

This Level 1 set tests the basics of statistics: finding the mean, median, mode and range of small data sets, along with simple variance and standard deviation. It is a free Aptitude360 practice quiz built on everyday data such as match scores, shoe sizes, temperatures and prices. Every question comes with a worked solution.

Topics covered in this Level 1 statistics set

  • Mean of raw data and of a simple frequency table
  • New mean after adding or removing one observation
  • Correcting a mean when a value was recorded wrongly
  • Median of odd and even sized data sets, including finding an unknown from a given median
  • Mode of ungrouped data and the empirical relation between mean, median and mode
  • Range, variance and standard deviation with the number of observations as divisor
  • Effect of adding, multiplying or dividing every observation on the mean, variance and standard deviation

Key formulas for mean, median and mode

  • Mean: \( \bar{x}=\dfrac{\sum x}{n} \)
  • Frequency mean: \( \bar{x}=\dfrac{\sum fx}{\sum f} \)
  • Empirical relation: \( \text{Mode}=3\,\text{Median}-2\,\text{Mean} \)
  • Range: \( \text{Max}-\text{Min} \)
  • Variance: \( \sigma^{2}=\dfrac{\sum (x-\bar{x})^{2}}{n} \)
  • If \( y=ax+b \): \( \bar{y}=a\bar{x}+b,\ \sigma_{y}=|a|\sigma_{x} \)

Revision tips for basic statistics

  • Always arrange the data in ascending order before finding the median.
  • For a corrected mean, fix the total first: subtract the wrong value, add the right one, then divide again.
  • Remember that adding a constant shifts the mean but leaves the standard deviation and variance unchanged.
  • When every value is divided by a number, the variance is divided by the square of that number.

Who this Level 1 set is for

Beginners in quantitative aptitude and school students meeting central tendency and dispersion for the first time should start here before moving on to the harder levels.

FAQs about Statistics: Mean, Median and Mode Practice Questions with Detailed Solutions – Level 1

What is the difference between mean, median and mode?
The mean is the sum of all values divided by the number of values. The median is the middle value when the data is arranged in order, and the mode is the value that occurs most often.
How do you find the median of an even number of observations?
Arrange the data in ascending order and take the average of the two middle values. That average is the median.
What is the empirical relation between mean, median and mode?
For a moderately skewed distribution, mode is approximately equal to three times the median minus two times the mean. It lets you find any one of the three measures when the other two are known.
Does adding a constant to every observation change the standard deviation?
No. Adding or subtracting the same constant shifts the mean by that constant, but the standard deviation and variance stay the same because the spread of the data does not change.

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 15050 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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