Mean, Median and Mode Notes for SSC Statistics
Rahul Kumar
SSC Exam Expert & Content Editor
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PDF Notes: Mean, Median and Mode Notes for SSC Statistics
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Mean, median and mode are the three measures of central tendency, and they form the first and most important chapter of SSC Statistics. A measure of central tendency gives one value that represents the whole data. Questions are asked on the formulas, the relation between the three measures and numerical problems on raw and grouped data. These mean, median and mode notes for SSC give every formula with solved examples and practice questions in simple language.
Three Measures of Central Tendency
| Measure | Meaning | Best used when |
|---|---|---|
| Mean (average) | Sum of all values divided by the number of values | Data has no extreme values |
| Median | Middle value after arranging the data in order | Data has very big or very small values |
| Mode | Value that occurs the most number of times | Most common item is needed |
Arithmetic Mean
| Case | Formula |
|---|---|
| Raw data | Mean = (x1 + x2 + ... + xn) / n |
| Frequency data | Mean = Σfx / Σf |
| Assumed mean method | Mean = A + Σfd / Σf, where d = x − A |
| Step deviation method | Mean = A + (Σfu / Σf) × h, where u = (x − A) / h |
| Weighted mean | Σwx / Σw |
| Combined mean of two groups | (n1 × mean1 + n2 × mean2) / (n1 + n2) |
- The sum of the deviations of all the values from the mean is always zero.
- If every value is increased by a number, the mean also increases by the same number.
- If every value is multiplied by a number, the mean is also multiplied by it.
Example 1. Find the mean of 5, 8, 11, 14 and 17.
Sum = 55 and n = 5, so mean = 11.
Example 2. The average marks of 10 students are 40 and the average marks of 20 students are 55. What is the combined mean?
(10 × 40 + 20 × 55) / 30 = 1500 / 30 = 50.
Median
- Arrange the values in ascending order.
- If n is odd, the median is the value at position (n + 1) / 2.
- If n is even, the median is the average of the values at positions n / 2 and (n / 2) + 1.
- For grouped data: Median = L + [(N / 2 − cf) / f] × h, where L is the lower limit of the median class, cf is the cumulative frequency before it, f is its frequency and h is the class width.
Example 3. Find the median of 3, 5, 7 and 9.
n = 4 is even, so median = (5 + 7) / 2 = 6.
Mode
- Mode is the value with the highest frequency, and data can have no mode, one mode or many modes.
- For grouped data: Mode = L + [(f1 − f0) / (2f1 − f0 − f2)] × h, where f1 is the frequency of the modal class, f0 is the frequency before it and f2 is the frequency after it.
Relation Between Mean, Median and Mode
| Relation | Meaning |
|---|---|
| Mode = 3 Median − 2 Mean | Empirical relation for a moderately skewed distribution |
| Mean = Median = Mode | Symmetric distribution |
| Mean > Median > Mode | Positively skewed distribution |
| Mean < Median < Mode | Negatively skewed distribution |
Example 4. If the mean is 30 and the median is 28, find the mode.
Mode = 3 × 28 − 2 × 30 = 84 − 60 = 24.
Other Averages
| Average | Formula for two numbers a and b |
|---|---|
| Geometric mean (GM) | √(ab) |
| Harmonic mean (HM) | 2ab / (a + b) |
| Order | AM ≥ GM ≥ HM; also GM² = AM × HM for two numbers |
- The geometric mean is used for averaging ratios and growth rates, and the harmonic mean is used for averaging speeds and rates.
Quick Tips
- Write the formula first, then put the numbers, because most mistakes come from wrong substitution.
- For grouped data, first find the cumulative frequency and the class with the highest frequency.
- Use the empirical relation to find any one of the three when two are given.
- Remember that the mean is affected by extreme values but the median and the mode are not.
Quick Revision Points
- Mean = sum of values / number of values.
- The sum of deviations from the mean is zero.
- Mode = 3 Median − 2 Mean.
- AM ≥ GM ≥ HM for positive numbers.
- Median is the best measure when there are extreme values.
Practice Questions With Answers
- Find the mean of 12, 15, 18, 20 and 25.
Answer: 18 - Find the median of 4, 9, 2, 7 and 6.
Answer: 6 (arranged as 2, 4, 6, 7, 9) - Find the mode of 3, 4, 4, 5, 6, 4, 7.
Answer: 4 - If the mean is 24 and the median is 22, find the mode (empirical).
Answer: 18 - What is the mean of the first 10 natural numbers?
Answer: 5.5 - The mean of 5 numbers is 20. If one number is removed, the mean becomes 18. Find the removed number.
Answer: 28 (100 − 72) - Which measure of central tendency is affected by extreme values the most?
Answer: Mean - Find the geometric mean of 4 and 9.
Answer: 6 - Find the harmonic mean of 2 and 6.
Answer: 3 - What is the relation between AM, GM and HM?
Answer: AM ≥ GM ≥ HM
How to Practise This Chapter
Solve five problems daily, two on raw data and three on grouped data, and always write the formula. Then solve the timed sets from our practice papers and the previous year papers page. Read the next chapter, Correlation and Regression, and see the full list on the Statistics notes page. For the maths basics, read the Average notes.
Frequently Asked Questions
What are measures of central tendency?
They are values that show the centre of the data. The three main ones are the mean, the median and the mode.
What is the formula of mean?
Mean is the sum of all the values divided by the number of values. For frequency data, it is the sum of f into x divided by the sum of f.
How do I find the median of an even number of values?
Arrange the values in order and take the average of the two middle values.
What is the mode?
The mode is the value which appears the maximum number of times in the data.
What is the empirical relation between mean, median and mode?
The relation is Mode = 3 Median minus 2 Mean. It is true for a moderately skewed distribution.
Which average is the best for data with extreme values?
The median is the best, because it is not affected by very big or very small values.
What is the weighted mean?
The weighted mean gives different importance to different values. It is the sum of weight into value divided by the sum of weights.
What is the sum of deviations from the mean?
The sum of the deviations of all the values from the mean is always zero.
What is the relation between AM, GM and HM?
For positive numbers, AM is greater than or equal to GM, and GM is greater than or equal to HM.
When is the mean equal to the median and the mode?
They are equal when the distribution is perfectly symmetric.
How should I prepare this chapter for SSC?
Learn the formulas, solve at least five numericals daily and practise grouped data problems, because they carry more marks.
How many questions come from this chapter in SSC Statistics?
Usually two to four questions come from measures of central tendency, but the number changes from year to year.
Rahul Kumar
SSC Exam Expert & Content Editor
Rahul is a senior SSC exam strategist with 8+ years of experience helping aspirants crack CGL, CHSL and MTS exams. He writes in-depth notification breakdowns, exam pattern guides and preparation strategies.