ICSE Class 10 Maths: Statistics — Mean, Median, Mode Notes 2026

Mean — Methods

• Direct method: mean = Σfx / Σf for grouped data
• Step-deviation method: a = assumed mean, h = class width; d = (x−a)/h; mean = a + h × Σfd/Σf
• Weighted mean for unequal weights: Σwx/Σw

Median for Grouped Data

• Arrange data in ascending order; median class: cumulative frequency just exceeds n/2
• Median formula: M = L + {(n/2 − cf)/f} × h where L = lower class boundary, cf = cumulative freq before median class
• For ungrouped data: middle value (n odd); average of two middle values (n even)

Mode for Grouped Data

• Modal class: class with highest frequency
• Mode = L + {(f₁ − f₀)/(2f₁ − f₀ − f₂)} × h (grouping formula)
• Relationship: Mean − Mode ≈ 3(Mean − Median) for moderately skewed data

Ogive (Cumulative Frequency Curve)

• Less than ogive: plot upper class boundary vs. cumulative frequency
• More than ogive: plot lower class boundary vs. cumulative frequency
• Intersection of less-than and more-than ogives gives median graphically

Quartiles and Percentiles

• Q₁ (lower quartile): n/4 value; Q₃ (upper quartile): 3n/4 value
• Inter-quartile range (IQR) = Q₃ − Q₁; measures spread of middle 50%
• Median = Q₂; percentile Pₖ = value below which k% of data falls

ICSE Exam: Step-by-Step

• Always prepare frequency table with class mark x, frequency f, cumulative frequency cf, fx columns
• For ogive: plot clearly labelled axes; identify quartiles from graph
• ICSE pattern: 1 question on mean by step-deviation, 1 on ogive for median and quartiles

Variance and Standard Deviation (Introduction)

• Variance = Σf(x−mean)²/Σf; SD = √Variance
• Low SD = data clustered near mean; high SD = data spread out
• ICSE does not require detailed calculation but conceptual understanding is expected