Concept Topic GuideCBSE & ICSEClass 10MathematicsStatisticsVerified Faculty Notes & Solutions
Statistics – Class 10 Maths Chapter 13: Mean, Median, Mode & Ogive
Class 10 Statistics notes: mean of grouped data (direct, assumed mean, step deviation), median, mode formulas, and ogive for CBSE & ICSE.
9 students readUpdated 4 September 2026
Chapter 13: Statistics
13.1 Mean of Grouped Data
Method 1: Direct Method
Mean (x̄) = Σfᵢxᵢ / Σfᵢ
Where xᵢ = class mark (midpoint) of each class = (upper limit + lower limit)/2, fᵢ = frequency
Where xᵢ = class mark (midpoint) of each class = (upper limit + lower limit)/2, fᵢ = frequency
Method 2: Assumed Mean Method
Mean = a + (Σfᵢdᵢ / Σfᵢ)
Where a = assumed mean (typically the class mark of the middle class), dᵢ = xᵢ − a
Where a = assumed mean (typically the class mark of the middle class), dᵢ = xᵢ − a
Method 3: Step-Deviation Method (Most efficient)
Mean = a + (Σfᵢuᵢ / Σfᵢ) × h
Where uᵢ = (xᵢ − a)/h, h = class size, a = assumed mean
Where uᵢ = (xᵢ − a)/h, h = class size, a = assumed mean
13.2 Mode of Grouped Data
The mode is the value that occurs most frequently. The modal class is the class with the highest frequency.
Mode = l + [(f₁ − f₀) / (2f₁ − f₀ − f₂)] × h
Where: l = lower limit of modal class, f₁ = frequency of modal class, f₀ = frequency of class before modal class, f₂ = frequency of class after modal class, h = class size
Where: l = lower limit of modal class, f₁ = frequency of modal class, f₀ = frequency of class before modal class, f₂ = frequency of class after modal class, h = class size
13.3 Median of Grouped Data
Median = l + [(n/2 − cf) / f] × h
Where: l = lower limit of median class, n = total frequency (Σfᵢ), cf = cumulative frequency of the class before the median class, f = frequency of the median class, h = class size
Where: l = lower limit of median class, n = total frequency (Σfᵢ), cf = cumulative frequency of the class before the median class, f = frequency of the median class, h = class size
Finding the median class: Calculate n/2. The class whose cumulative frequency is just greater than or equal to n/2 is the median class.
13.4 Empirical Relationship
3 Median = Mode + 2 Mean
This approximate relationship helps verify your calculations and is useful when one of the three measures is difficult to compute directly.
This approximate relationship helps verify your calculations and is useful when one of the three measures is difficult to compute directly.
13.5 Ogive (Cumulative Frequency Curve)
An ogive is a graph of cumulative frequency against upper class boundaries.
- Less-than ogive: Plot cumulative frequencies against upper class limits — curve rises from left to right.
- More-than ogive: Plot cumulative frequencies against lower class limits — curve falls from left to right.
- The median can be found from the point where the two ogives intersect, or by drawing a horizontal line from n/2 on the y-axis to the less-than ogive and reading the x-coordinate.
Indexed Topics & Examination Keywords
#statistics class 10#mean median mode#grouped data#assumed mean method#step deviation#ogive#NCERT maths#CBSE#ICSE#cumulative frequency
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