Statistics is an important mathematics topic for school exams, competitive exams, entrance tests and aptitude preparation. It is useful because many questions can be solved quickly when the definitions, formulas and examples are understood properly.
This tutorial explains statistics in simple language. It includes meaning, important terms, formulas, step-by-step methods, shortcut ideas, solved examples, practice questions, answers, common mistakes and FAQs.
The best way to learn statistics is to first understand the rule, then solve easy examples, and then try exam-style questions. This page follows the same order.
What Is Statistics?
Statistics is the study of collecting, organising, presenting, analysing and interpreting data.
Important Terms
| Point | Details |
|---|---|
| Data | Collection of values |
| Mean | Average value |
| Median | Middle value |
| Mode | Most repeated value |
| Range | Highest value minus lowest value |
Important Formulas and Rules
| Point | Details |
|---|---|
| Mean | Sum of observations / Number of observations |
| Median odd count | Middle observation after arranging |
| Median even count | Average of two middle observations |
| Mode | Most frequent value |
| Range | Maximum – Minimum |
Step-by-Step Method
- Arrange data if median is required.
- Find sum and count for mean.
- Find middle value for median.
- Find most repeated value for mode.
- Subtract smallest from largest for range.
Shortcut Ideas
- Mean is affected by very large or small values.
- Median needs arranged data.
- Mode can be more than one value.
- Range measures spread.
- Frequency table helps count repeated values.
Common Question Types
| Point | Details |
|---|---|
| Mean | Average |
| Median | Middle value |
| Mode | Most common value |
| Range | Spread |
| Frequency table | Grouped counting |
Solved Examples
Example 1
Mean of 2,4,6.
Mean = 12/3 = 4.
Example 2
Median of 3,7,9.
Median = 7.
Example 3
Mode of 2,2,3,4.
Mode = 2.
Example 4
Range of 5,9,12.
12 – 5 = 7.
Example 5
Median of 2,4,6,8.
(4+6)/2 = 5.
Exam Style Examples
Question 1
Find mean of 10,20,30,40.
Mean = 100/4 = 25.
Mean is average.
Question 2
Find median of 8,3,5,9,1.
Arrange 1,3,5,8,9. Median = 5.
Arrange first.
Question 3
Find mode of 4,5,5,6,6,6,7.
Mode = 6.
Mode appears most often.
Common Mistakes
- Finding median without arranging data.
- Confusing mean and mode.
- Forgetting to divide mean by count.
- Taking range as highest plus lowest.
- Ignoring repeated values.
Practice Questions
- Mean of 5,10,15.
- Median of 1,3,5.
- Mode of 2,3,3,4.
- Range of 10,20,35.
- Median of 2,4,6,8.
- Mean of 6,6,6.
- Mode of 1,1,2,2,3.
- Range of 5,5,5.
- Mean of 100 and 200.
- Median of 9,1,7.
Answers to Practice Questions
- 10
- 3
- 3
- 25
- 5
- 6
- 1 and 2
- 0
- 150
- 7
Frequently Asked Questions
What is statistics?
It is the study of data.
What is mean?
Mean is average.
What is median?
Median is middle value after arranging data.
What is mode?
Mode is most repeated value.
What is range?
Range is highest value minus lowest value.
Revision Notes
Statistics starts with arranging and counting data correctly. Mean, median, mode and range answer different questions.
For revision, keep a small formula list and solve a few mixed questions. Do not only read the solution. Try the question first, then compare your steps with the answer.
Conclusion
Statistics becomes easy when each measure is used for the correct purpose.
Additional Exam Notes
Statistics questions should be solved with a clear setup. First identify the given values, then decide which formula or property is useful. If the expression has variables, write each step neatly so sign mistakes can be avoided.
Many students lose marks because they know the formula but apply it too quickly. Slow reading at the start saves time later. Check whether the question asks for value, root, degree, distance, slope, mean, median, mode, area or final conclusion.
After solving, verify the answer by substitution, estimation or unit checking. This is especially useful in algebra and coordinate geometry, where one wrong sign can change the whole answer.
Additional Exam Notes
Statistics questions should be solved with a clear setup. First identify the given values, then decide which formula or property is useful. If the expression has variables, write each step neatly so sign mistakes can be avoided.
Many students lose marks because they know the formula but apply it too quickly. Slow reading at the start saves time later. Check whether the question asks for value, root, degree, distance, slope, mean, median, mode, area or final conclusion.
After solving, verify the answer by substitution, estimation or unit checking. This is especially useful in algebra and coordinate geometry, where one wrong sign can change the whole answer.
Additional Exam Notes
Statistics questions should be solved with a clear setup. First identify the given values, then decide which formula or property is useful. If the expression has variables, write each step neatly so sign mistakes can be avoided.
Many students lose marks because they know the formula but apply it too quickly. Slow reading at the start saves time later. Check whether the question asks for value, root, degree, distance, slope, mean, median, mode, area or final conclusion.
After solving, verify the answer by substitution, estimation or unit checking. This is especially useful in algebra and coordinate geometry, where one wrong sign can change the whole answer.
Additional Exam Notes
Statistics questions should be solved with a clear setup. First identify the given values, then decide which formula or property is useful. If the expression has variables, write each step neatly so sign mistakes can be avoided.
Many students lose marks because they know the formula but apply it too quickly. Slow reading at the start saves time later. Check whether the question asks for value, root, degree, distance, slope, mean, median, mode, area or final conclusion.
After solving, verify the answer by substitution, estimation or unit checking. This is especially useful in algebra and coordinate geometry, where one wrong sign can change the whole answer.
Additional Exam Notes
Statistics questions should be solved with a clear setup. First identify the given values, then decide which formula or property is useful. If the expression has variables, write each step neatly so sign mistakes can be avoided.
Many students lose marks because they know the formula but apply it too quickly. Slow reading at the start saves time later. Check whether the question asks for value, root, degree, distance, slope, mean, median, mode, area or final conclusion.
After solving, verify the answer by substitution, estimation or unit checking. This is especially useful in algebra and coordinate geometry, where one wrong sign can change the whole answer.
Additional Exam Notes
Statistics questions should be solved with a clear setup. First identify the given values, then decide which formula or property is useful. If the expression has variables, write each step neatly so sign mistakes can be avoided.
Many students lose marks because they know the formula but apply it too quickly. Slow reading at the start saves time later. Check whether the question asks for value, root, degree, distance, slope, mean, median, mode, area or final conclusion.
After solving, verify the answer by substitution, estimation or unit checking. This is especially useful in algebra and coordinate geometry, where one wrong sign can change the whole answer.
Additional Exam Notes
Statistics questions should be solved with a clear setup. First identify the given values, then decide which formula or property is useful. If the expression has variables, write each step neatly so sign mistakes can be avoided.
Many students lose marks because they know the formula but apply it too quickly. Slow reading at the start saves time later. Check whether the question asks for value, root, degree, distance, slope, mean, median, mode, area or final conclusion.
After solving, verify the answer by substitution, estimation or unit checking. This is especially useful in algebra and coordinate geometry, where one wrong sign can change the whole answer.
Additional Exam Notes
Statistics questions should be solved with a clear setup. First identify the given values, then decide which formula or property is useful. If the expression has variables, write each step neatly so sign mistakes can be avoided.
Many students lose marks because they know the formula but apply it too quickly. Slow reading at the start saves time later. Check whether the question asks for value, root, degree, distance, slope, mean, median, mode, area or final conclusion.
After solving, verify the answer by substitution, estimation or unit checking. This is especially useful in algebra and coordinate geometry, where one wrong sign can change the whole answer.
Additional Exam Notes
Statistics questions should be solved with a clear setup. First identify the given values, then decide which formula or property is useful. If the expression has variables, write each step neatly so sign mistakes can be avoided.
Many students lose marks because they know the formula but apply it too quickly. Slow reading at the start saves time later. Check whether the question asks for value, root, degree, distance, slope, mean, median, mode, area or final conclusion.
After solving, verify the answer by substitution, estimation or unit checking. This is especially useful in algebra and coordinate geometry, where one wrong sign can change the whole answer.
Additional Exam Notes
Statistics questions should be solved with a clear setup. First identify the given values, then decide which formula or property is useful. If the expression has variables, write each step neatly so sign mistakes can be avoided.
Many students lose marks because they know the formula but apply it too quickly. Slow reading at the start saves time later. Check whether the question asks for value, root, degree, distance, slope, mean, median, mode, area or final conclusion.
After solving, verify the answer by substitution, estimation or unit checking. This is especially useful in algebra and coordinate geometry, where one wrong sign can change the whole answer.
Additional Exam Notes
Statistics questions should be solved with a clear setup. First identify the given values, then decide which formula or property is useful. If the expression has variables, write each step neatly so sign mistakes can be avoided.
Many students lose marks because they know the formula but apply it too quickly. Slow reading at the start saves time later. Check whether the question asks for value, root, degree, distance, slope, mean, median, mode, area or final conclusion.
After solving, verify the answer by substitution, estimation or unit checking. This is especially useful in algebra and coordinate geometry, where one wrong sign can change the whole answer.
Additional Exam Notes
Statistics questions should be solved with a clear setup. First identify the given values, then decide which formula or property is useful. If the expression has variables, write each step neatly so sign mistakes can be avoided.
Many students lose marks because they know the formula but apply it too quickly. Slow reading at the start saves time later. Check whether the question asks for value, root, degree, distance, slope, mean, median, mode, area or final conclusion.
After solving, verify the answer by substitution, estimation or unit checking. This is especially useful in algebra and coordinate geometry, where one wrong sign can change the whole answer.
Additional Exam Notes
Statistics questions should be solved with a clear setup. First identify the given values, then decide which formula or property is useful. If the expression has variables, write each step neatly so sign mistakes can be avoided.
Many students lose marks because they know the formula but apply it too quickly. Slow reading at the start saves time later. Check whether the question asks for value, root, degree, distance, slope, mean, median, mode, area or final conclusion.
After solving, verify the answer by substitution, estimation or unit checking. This is especially useful in algebra and coordinate geometry, where one wrong sign can change the whole answer.
Additional Exam Notes
Statistics questions should be solved with a clear setup. First identify the given values, then decide which formula or property is useful. If the expression has variables, write each step neatly so sign mistakes can be avoided.
Many students lose marks because they know the formula but apply it too quickly. Slow reading at the start saves time later. Check whether the question asks for value, root, degree, distance, slope, mean, median, mode, area or final conclusion.
After solving, verify the answer by substitution, estimation or unit checking. This is especially useful in algebra and coordinate geometry, where one wrong sign can change the whole answer.
Additional Exam Notes
Statistics questions should be solved with a clear setup. First identify the given values, then decide which formula or property is useful. If the expression has variables, write each step neatly so sign mistakes can be avoided.
Many students lose marks because they know the formula but apply it too quickly. Slow reading at the start saves time later. Check whether the question asks for value, root, degree, distance, slope, mean, median, mode, area or final conclusion.
After solving, verify the answer by substitution, estimation or unit checking. This is especially useful in algebra and coordinate geometry, where one wrong sign can change the whole answer.
Additional Exam Notes
Statistics questions should be solved with a clear setup. First identify the given values, then decide which formula or property is useful. If the expression has variables, write each step neatly so sign mistakes can be avoided.
Many students lose marks because they know the formula but apply it too quickly. Slow reading at the start saves time later. Check whether the question asks for value, root, degree, distance, slope, mean, median, mode, area or final conclusion.
After solving, verify the answer by substitution, estimation or unit checking. This is especially useful in algebra and coordinate geometry, where one wrong sign can change the whole answer.
Additional Exam Notes
Statistics questions should be solved with a clear setup. First identify the given values, then decide which formula or property is useful. If the expression has variables, write each step neatly so sign mistakes can be avoided.
Many students lose marks because they know the formula but apply it too quickly. Slow reading at the start saves time later. Check whether the question asks for value, root, degree, distance, slope, mean, median, mode, area or final conclusion.
After solving, verify the answer by substitution, estimation or unit checking. This is especially useful in algebra and coordinate geometry, where one wrong sign can change the whole answer.
Additional Exam Notes
Statistics questions should be solved with a clear setup. First identify the given values, then decide which formula or property is useful. If the expression has variables, write each step neatly so sign mistakes can be avoided.
Many students lose marks because they know the formula but apply it too quickly. Slow reading at the start saves time later. Check whether the question asks for value, root, degree, distance, slope, mean, median, mode, area or final conclusion.
After solving, verify the answer by substitution, estimation or unit checking. This is especially useful in algebra and coordinate geometry, where one wrong sign can change the whole answer.
Additional Exam Notes
Statistics questions should be solved with a clear setup. First identify the given values, then decide which formula or property is useful. If the expression has variables, write each step neatly so sign mistakes can be avoided.
Many students lose marks because they know the formula but apply it too quickly. Slow reading at the start saves time later. Check whether the question asks for value, root, degree, distance, slope, mean, median, mode, area or final conclusion.
After solving, verify the answer by substitution, estimation or unit checking. This is especially useful in algebra and coordinate geometry, where one wrong sign can change the whole answer.
Additional Exam Notes
Statistics questions should be solved with a clear setup. First identify the given values, then decide which formula or property is useful. If the expression has variables, write each step neatly so sign mistakes can be avoided.
Many students lose marks because they know the formula but apply it too quickly. Slow reading at the start saves time later. Check whether the question asks for value, root, degree, distance, slope, mean, median, mode, area or final conclusion.
After solving, verify the answer by substitution, estimation or unit checking. This is especially useful in algebra and coordinate geometry, where one wrong sign can change the whole answer.
Additional Exam Notes
Statistics questions should be solved with a clear setup. First identify the given values, then decide which formula or property is useful. If the expression has variables, write each step neatly so sign mistakes can be avoided.
Many students lose marks because they know the formula but apply it too quickly. Slow reading at the start saves time later. Check whether the question asks for value, root, degree, distance, slope, mean, median, mode, area or final conclusion.
After solving, verify the answer by substitution, estimation or unit checking. This is especially useful in algebra and coordinate geometry, where one wrong sign can change the whole answer.
Additional Exam Notes
Statistics questions should be solved with a clear setup. First identify the given values, then decide which formula or property is useful. If the expression has variables, write each step neatly so sign mistakes can be avoided.
Many students lose marks because they know the formula but apply it too quickly. Slow reading at the start saves time later. Check whether the question asks for value, root, degree, distance, slope, mean, median, mode, area or final conclusion.
After solving, verify the answer by substitution, estimation or unit checking. This is especially useful in algebra and coordinate geometry, where one wrong sign can change the whole answer.
Additional Exam Notes
Statistics questions should be solved with a clear setup. First identify the given values, then decide which formula or property is useful. If the expression has variables, write each step neatly so sign mistakes can be avoided.
Many students lose marks because they know the formula but apply it too quickly. Slow reading at the start saves time later. Check whether the question asks for value, root, degree, distance, slope, mean, median, mode, area or final conclusion.
After solving, verify the answer by substitution, estimation or unit checking. This is especially useful in algebra and coordinate geometry, where one wrong sign can change the whole answer.
Additional Exam Notes
Statistics questions should be solved with a clear setup. First identify the given values, then decide which formula or property is useful. If the expression has variables, write each step neatly so sign mistakes can be avoided.
Many students lose marks because they know the formula but apply it too quickly. Slow reading at the start saves time later. Check whether the question asks for value, root, degree, distance, slope, mean, median, mode, area or final conclusion.
After solving, verify the answer by substitution, estimation or unit checking. This is especially useful in algebra and coordinate geometry, where one wrong sign can change the whole answer.