10
CBSE Marks
★★★★★
Difficulty
9
Topics
High
Board Weight
Topics Covered
9 key topics in this chapter
Mean of Grouped Data: Direct Method
Assumed Mean Method
Step-Deviation Method
Mode of Grouped Data
Median of Grouped Data
Cumulative Frequency Table
Less Than & More Than Ogive
Median from Ogive
Relationship: Mean, Median, Mode
Study Resources
Key Formulas
| Formula / Rule | Expression |
|---|---|
| Mean (Direct) | \(x̄ = Σfᵢxᵢ / Σfᵢ\) |
| Mean (Assumed) | \(x̄ = a + (Σfᵢdᵢ / Σfᵢ)\) |
| Mean (Step Dev) | \(x̄ = a + h·(Σfᵢuᵢ / Σfᵢ)\) |
| Mode | \(l + [(f₁−f₀)/(2f₁−f₀−f₂)]·h\) |
| Median | \(l + [(n/2−cf)/f]·h\) |
| Empirical Relation | \(Mode ≈ 3·Median − 2·Mean\) |
Important Points to Remember
For grouped data, the class mark (midpoint) is used as xᵢ in the direct and assumed mean methods.
Step-deviation method is most efficient when class widths are equal.
Mode is the value with the highest frequency; for grouped data, use the modal class formula.
Median divides the total area of the histogram into two equal halves.