CBSE · Class 10
Statistics Formulas for Class 10
Mean, Median, Mode of grouped data — all three methods for CBSE Class 10 Maths Chapter 14
Ch 1.Mean of Grouped Data
| Formula / Relation | Expression |
|---|---|
| Direct Method | Mean (x̄) = Σfᵢxᵢ / Σfᵢ |
| Assumed Mean Method | Mean (x̄) = a + (Σfᵢdᵢ / Σfᵢ) |
| Step Deviation Method | Mean (x̄) = a + (Σfᵢuᵢ / Σfᵢ) × h |
| Class mark (midpoint) | xᵢ = (lower class limit + upper class limit) / 2 |
Ch 2.Median of Grouped Data
| Formula / Relation | Expression |
|---|---|
| Median formula | Median = l + [(n/2 − cf) / f] × h |
| Locating median class | Find class whose cumulative frequency ≥ n/2 for the first time |
Ch 3.Mode of Grouped Data
| Formula / Relation | Expression |
|---|---|
| Mode formula | Mode = l + [(f₁ − f₀) / (2f₁ − f₀ − f₂)] × h |
| Modal class | Class with the highest frequency |
Ch 4.Empirical Relationship
| Formula / Relation | Expression |
|---|---|
| Mean, Median, Mode relation | Mode = 3 × Median − 2 × Mean |
| Alternative form | Median = (Mode + 2 × Mean) / 3 |
Ch 5.Cumulative Frequency and Ogive
| Formula / Relation | Expression |
|---|---|
| Less than ogive | Plot (upper class boundary, cumulative frequency) for each class |
| More than ogive | Plot (lower class boundary, total − cumulative frequency) for each class |
| Median from ogive | Intersection of less-than and more-than ogives gives median on x-axis |
Ch 6.Probability (Class 10 — Chapter 15)
| Formula / Relation | Expression |
|---|---|
| Probability of event E | P(E) = Number of favourable outcomes / Total number of equally likely outcomes |
| Range of probability | 0 ≤ P(E) ≤ 1 |
| Complementary event | P(Ē) = 1 − P(E) |
| Sum of all probabilities | P(E₁) + P(E₂) + ... + P(Eₙ) = 1 |
Frequently Asked Questions
What are the three methods to find mean in Class 10 Statistics?
Three methods: (1) Direct Method: x̄ = Σfᵢxᵢ / Σfᵢ — multiply each class mark by its frequency, sum up, divide by total frequency. (2) Assumed Mean Method: x̄ = a + Σfᵢdᵢ/Σfᵢ — choose a central class mark as 'a', compute deviations. (3) Step Deviation Method: x̄ = a + (Σfᵢuᵢ/Σfᵢ)×h — divide deviations by class width h. All three give the same answer; Step Deviation is fastest with uniform class widths.
What is the formula for median of grouped data in Class 10?
Median = l + [(n/2 − cf) / f] × h. Where: l = lower boundary of median class, n = total frequency, cf = cumulative frequency of class BEFORE the median class, f = frequency of median class, h = class width. First find n/2, then identify which class has cumulative frequency ≥ n/2 for the first time — that is the median class.
What is the empirical relationship between mean, median, and mode?
Mode = 3 × Median − 2 × Mean. This is an empirical (observed) formula, not an exact mathematical proof. It holds approximately for unimodal, moderately skewed distributions. In CBSE Class 10, you are expected to use this formula to find the third average when two are given. Example: if Mean = 60 and Mode = 54, then Median = (Mode + 2×Mean)/3 = (54+120)/3 = 58.
How is the mode of grouped data calculated?
Mode = l + [(f₁−f₀)/(2f₁−f₀−f₂)] × h. Find the modal class (highest frequency class) first. Then: l = lower boundary of modal class, f₁ = frequency of modal class, f₀ = frequency of class before modal class, f₂ = frequency of class after modal class, h = class width. If two classes have the same highest frequency, it is a bimodal distribution and this formula gives one mode only.
How do you draw an ogive for Class 10 Statistics?
Less than ogive: plot upper class boundary on x-axis and cumulative frequency on y-axis. More than ogive: plot lower class boundary on x-axis and 'more than' cumulative frequency (total minus cf) on y-axis. Where the two ogives intersect, drop a perpendicular to the x-axis — that x-coordinate is the median. This graphical method is a standard CBSE board question.
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