Statistics Tests — Pick a Level and Start
Tap a level to see every test in it. Level 1 is set at real SSC CGL difficulty — start there the day you finish the concept. Level 2 is pitched above the exam, to push accuracy under pressure.
Level 1 SSC CGL Level Checking… View tests
Same difficulty as the real SSC CGL paper — one formula applied cleanly. The mean of a list and of a frequency table; the assumed-mean and step-deviation shortcuts; a missing value or frequency from a given mean; the effect of adding or multiplying every value; a misread observation corrected; combined means of two groups; the median of odd, even and grouped data; the mode of a list and of a grouped table; Mode = 3 Median − 2 Mean; range, class marks and true boundaries; mean deviation; variance and standard deviation from raw data or from Σx and Σx²; the SD of 1, 2, …, n; the coefficient of variation; quartiles; Pearson's skewness; and AM, GM and HM. A steady score here means the chapter is exam-ready.
Level 2 Above SSC CGL Level Checking… View tests
Harder than the exam asks, because every question chains two results or runs one backwards. Two unknown frequencies from the total and the mean; a missing frequency from a given median or mode; the class width recovered from the mode; a group size or a missing group SD from the combined variance; the count n from a corrected mean; a corrected variance rebuilt from Σx and Σx²; y = ax + b recovered from two means and two SDs; two numbers from their AM and HM; a mode, then the direction of skew; percentiles and deciles with interpolation; and the median after a bonus and a pass mark. Clear these and the real paper feels easy.
A statistics question is almost always one formula in disguise. Once you see what is being asked — a centre (mean, median, mode), a spread (range, mean deviation, standard deviation) or a comparison (coefficient of variation, skewness) — the working is short. The skill is reading the data shape before you calculate: a raw list, a discrete frequency table and a grouped table each need a different version of the same formula, and inclusive classes need true boundaries first.
The marks are lost in three places. The first is forgetting to sort — the median is the middle of the ordered list, and the median of two merged lists is never the average of their two medians. The second is mixing up variance and standard deviation: variance is the square, so multiplying every value by 3 multiplies the SD by 3 but the variance by 9, while adding a constant changes neither. The third is treating a combined mean as a simple average — groups of different sizes must be weighted by their sizes. Each test puts twenty-five statistics questions in front of you in one sitting, which is what makes those checks automatic.
How Many Statistics Questions Are Asked in SSC CGL?
Statistics is a small but reliable chapter. Tier I asks it only occasionally, while Tier II Paper I lists statistics in its syllabus and usually has one or two questions — quick marks for anyone who knows the formulas.
| Chapter | Tier I (out of 25) | Tier II Paper I (out of 30) |
|---|---|---|
| Statistics (mean, median, mode, dispersion) | 0–1 | 1–2 |
| Average | 1–2 | 1–2 |
Counts vary by shift. Every mean question in statistics is built on the average chapter, so the two are best prepared back to back.
What You Will Practice in the Statistics Chapter
Mean and its shortcuts
- The mean of a list, of expressions in x, and of the first n natural, odd or even numbers
- Discrete and grouped frequency tables — direct, assumed-mean and step-deviation methods
- A missing value or a missing frequency from a given mean, including two unknown frequencies
- Adding, multiplying or linearly changing every value, and working backwards to the constant
- Misread, omitted or double-counted observations, and observations added or removed
- Combined means of two or three groups, group sizes, fractions of a class and overlapping blocks
Median, mode and grouped data
- The median of odd, even, repeated and unsorted lists, and of numbers in an arithmetic pattern
- The median of grouped, less-than and more-than cumulative tables; a missing frequency from the median
- The mode of a list, bimodal lists, and the grouped-mode formula with its edge cases
- Mode = 3 Median − 2 Mean, ratios of the three measures and their order in skewed data
- Range, coefficient of range, class marks, widths and true class boundaries
- Quartiles, deciles, percentiles and the quartile deviation
Dispersion and comparison
- Mean deviation about the mean and the median, and its coefficient
- Variance and standard deviation from raw data, from Σx and Σx², and in surd form
- The SD of 1, 2, …, n and of any arithmetic progression
- Change of origin and scale — what adding, multiplying or flipping the sign does to SD and variance
- The coefficient of variation and comparing the consistency of two series
- Pearson's coefficient of skewness, AM ≥ GM ≥ HM, and the combined variance of two groups
Formulas worth memorising
| Situation | Formula |
|---|---|
| Mean of a frequency table | x̄ = Σfx ÷ Σf |
| Step-deviation (assumed mean A, width h) | x̄ = A + (Σfu ÷ Σf) × h |
| Combined mean | (n₁x̄₁ + n₂x̄₂) ÷ (n₁ + n₂) |
| Median of grouped data | L + ((N/2 − cf) ÷ f) × h |
| Mode of grouped data | L + ((f₁ − f₀) ÷ (2f₁ − f₀ − f₂)) × h |
| Empirical relation | Mode = 3 Median − 2 Mean |
| Variance | σ² = Σx²/n − x̄² |
| SD of 1, 2, …, n | σ = √((n² − 1)/12); for an AP multiply by the common difference |
| Change of origin and scale | SD(a + bx) = |b| × SD(x), variance × b² |
| Coefficient of variation | CV = (σ ÷ x̄) × 100 |
| Combined variance | [n₁(σ₁² + d₁²) + n₂(σ₂² + d₂²)] ÷ (n₁ + n₂) |
| Skewness (Pearson) | (Mean − Mode) ÷ σ or 3(Mean − Median) ÷ σ |
| Quartile deviation | (Q₃ − Q₁) ÷ 2 |
| Two positive numbers | AM ≥ GM ≥ HM and GM² = AM × HM |
In the combined-variance row, d₁ and d₂ are each group's distance from the combined mean. The first six rows cover most Tier I questions; the rest are the Tier II core.
The three mistakes that cost the most marks
- Taking the middle of an unsorted list. Always sort first. For an even count, the median is the mean of the two middle values, which may not be in the data at all.
- Squaring in the wrong place. Multiplying every value by k multiplies the SD by |k| but the variance by k². Adding a constant changes the mean, median and mode but not the spread.
- Averaging averages. A combined mean, combined variance or overall mean of fractions of a class must be weighted by the group sizes; averaging the group figures directly is right only when the groups are equal.
Solved Examples — SSC CGL Statistics Questions
(30 × 62 + 20 × 57) ÷ 50 = (1860 + 1140) ÷ 50 = 60. The simple average of 62 and 57 (59.5) is wrong because the sections are not the same size. Answer: 60N = 40, so N/2 = 20. The cumulative frequencies are 6, 16, 32, …, so the median class is 20–30 with cf = 16 and f = 16. Median = 20 + ((20 − 16) ÷ 16) × 10 = 22.5. Answer: 22.5Mode = 3 × 34 − 2 × 36 = 102 − 72 = 30. Mean > median > mode, so the distribution is positively skewed. Answer: 30SD(y) = |−2| × 5 = 10, so the variance is 10² = 100. Answer: SD 10, variance 100How the Statistics Chapter Tests Work
- 25 questions per test, with a full question palette — answered, skipped, marked for review, not visited.
- Frequency tables written into the question, so every value you need is on screen with the question.
- Optional 15-minute timer — with the clock to build exam speed, without it while you are still learning the chapter.
- Marking: +2 correct, −0.5 wrong, 0 unattempted — the same scheme as the real paper.
- Solutions, shortcut tricks and concept notes open after you submit, question by question.
- English and हिंदी, chosen at the start of every test.
- Free with a TrickySSC account — sign in once with Google or your mobile number, and every test is open to you.
How to Prepare Statistics for SSC CGL
- Decide the data shape first. A raw list, a discrete table and a grouped table each use a different form of the same formula; inclusive classes need true boundaries before the median or mode.
- Sort before you look for the middle. Write the list in order every time, including any repeats and any value you had to solve for.
- Work with totals, not means. Sum = mean × count turns corrected-mean, added-value and combined-mean questions into simple addition and subtraction.
- Use the assumed-mean shortcut. Subtract a central value and divide by the class width; the smaller numbers cut calculation errors.
- Learn the empirical relation both ways. Mode = 3 Median − 2 Mean, and Median = (Mode + 2 Mean) ÷ 3; the median sits two-thirds of the way from the mode to the mean.
- Keep variance and SD apart. Write σ or σ² before every number; change of scale multiplies one by |k| and the other by k².
- Memorise √((n² − 1)/12). It gives the SD of 1 to n instantly, and multiplying by the common difference gives the SD of any evenly spaced list.
- Compare consistency with CV, not SD. The series with the smaller coefficient of variation is more consistent, even if its standard deviation is larger.
- Do Level 1 untimed, the same day you finish the theory. It is set at real SSC CGL difficulty; the aim is choosing the right formula, not speed.
- Repeat Level 1 with the 15-minute clock on, then move to Level 2. After that, verify against a previous year paper and a full mock test under locked sectional timing.
All SSC CGL Chapter Wise Tests
Every chapter below has its own free Level 1 and Level 2 tests with full solutions.
Browse all 45 chapter tests — Maths (35) · Reasoning (10)
- Number System
- Rule of Divisibility
- Remainder Theorem
- Decimal & Fraction
- LCM & HCF
- Square & Cube Root
- Number Series (AP & GP)
- Power, Indices & Surds
- Algebraic Formula
- Algebraic Result
- Algebraic Expression & Identities
- Percentage
- Profit & Loss
- Discount & Marked Price
- Simple Interest
- Compound Interest
- Ratio & Proportion
- Partnership
- Average
- Problems on Ages
- Mixture & Alligation
- Time & Work
- Pipe and Cistern
- Time, Speed and Distance
- Quadratic Equation
- Boat and Stream
- Races
- Trigonometry
- Heights & Distances
- Geometry
- Mensuration
- Coordinate Geometry
- Probability
- Statistics
- Data Interpretation
- All Maths chapters →
SSC CGL सांख्यिकी (Statistics) चैप्टर टेस्ट — हिंदी में
सांख्यिकी का लगभग हर प्रश्न किसी एक सूत्र का रूप होता है। पहले देखें कि प्रश्न केंद्र पूछ रहा है — माध्य (MEAN), माध्यिका (MEDIAN), बहुलक (MODE) — या फैलाव — परिसर (RANGE), माध्य विचलन (MEAN DEVIATION), मानक विचलन (STANDARD DEVIATION) — या तुलना — विचरण गुणांक (COEFFICIENT OF VARIATION), विषमता (SKEWNESS)। फिर हल छोटा होता है, जैसे बहुलक = 3 माध्यिका − 2 माध्य।
अंक तीन जगह कटते हैं। पहली: क्रम लगाए बिना बीच का मान लेना — माध्यिका हमेशा क्रमबद्ध सूची का बीच होती है। दूसरी: प्रसरण (VARIANCE) और मानक विचलन को मिला देना — हर मान को 3 से गुणा करने पर SD 3 गुना पर प्रसरण 9 गुना होता है, और अचर जोड़ने से दोनों नहीं बदलते। तीसरी: अलग आकार के समूहों के माध्यों का सीधा माध्य लेना — संयुक्त माध्य समूहों के आकार से भारित होता है।
TrickySSC पर इस अध्याय के सभी टेस्ट हिंदी में उपलब्ध हैं — प्रश्न, विकल्प, विस्तृत हल और शॉर्टकट ट्रिक सब हिंदी में। दो स्तर हैं: लेवल 1 (SSC CGL के स्तर का) और लेवल 2 (SSC CGL से कठिन)। प्रत्येक टेस्ट में 25 प्रश्न, वैकल्पिक 15 मिनट का टाइमर और +2 / −0.5 की वही मार्किंग जो असली परीक्षा में होती है।