Descriptive Stats · Combinatorics · Basic Probability
Quick Answer – What are Descriptive Statistics & Probability?
Descriptive statistics summarise data using measures like mean, median, mode, variance, and standard deviation. Permutations (nPr) count ordered arrangements, while combinations (nCr) count unordered selections. Probability of an event is the ratio of favourable outcomes to total possible outcomes.
Key Formulas
Mean (μ) = (Σ xi) / n
Variance (σ²) = Σ (xi − μ)² / n
nPr = n! / (n−r)! nCr = n! / [r!(n−r)!]
P(Event) = Favourable outcomes / Total outcomes
Solved Examples
Example 1: Dataset [4, 8, 6, 5, 3]
Mean = (4+8+6+5+3)/5 = 26/5 = 5.2
Sorted: 3,4,5,6,8 → Median = 5
Mode = none (all unique)
Variance = ((4-5.2)²+(8-5.2)²+...)/5 = 3.36
Example 2: 7P3
7P3 = 7!/(7-3)! = 7×6×5 = 210
Example 3: Probability of drawing an ace from a deck
Favourable = 4, Total = 52 → P = 4/52 = 1/13 ≈ 0.0769
Frequently Asked Questions
Q1. How do I enter the dataset?
Type numbers separated by commas (e.g., 5, 8.2, -3). Spaces are ignored. You can use decimals and negatives.
Q2. What if my dataset has multiple modes?
The calculator will display all modes if there are ties. If no number repeats, it shows "No mode".
Q3. Are nPr and nCr computed for large numbers?
Yes, but be careful with very large n (e.g., n>170) as factorials grow huge; the tool may show "Infinity". For practical JEE/NCERT values, it works perfectly.
Q4. What if I enter a negative probability or r > n?
The calculator validates inputs: r must be ≤ n, and probabilities must be between 0 and 1 (favourable ≤ total, non‑negative). It will show an error if constraints are violated.
Q5. Does variance use population or sample formula?
This calculator uses the population variance (dividing by n). For sample variance, multiply the result by n/(n−1).