9
CBSE Marks
★★★★★
Difficulty
9
Topics
High
Board Weight
Topics Covered
9 key topics in this chapter
Collection of Data
Presentation of Data
Frequency Distribution Table
Grouped & Ungrouped Data
Bar Graphs & Histograms
Frequency Polygons
Mean of Ungrouped Data
Median of Ungrouped Data
Mode of Ungrouped Data
Study Resources
Key Formulas & Identities
| Formula / Rule | Expression |
|---|---|
| Mean (ungrouped) | \(x̄ = (x₁+x₂+…+xₙ) / n = Σxᵢ / n\) |
| Mean (frequency) | \(x̄ = Σfᵢxᵢ / Σfᵢ\) |
| Median (odd n) | \(M = value at position (n+1)/2\) |
| Median (even n) | \(M = average of n/2 th and (n/2+1)th values\) |
| Mode | \(Value(s) with highest frequency\) |
| Range | \(Max value − Min value\) |
| Class mark | \((Lower limit + Upper limit) / 2\) |
| Class width | \(Upper limit − Lower limit\) |
Important Points to Remember
For ungrouped data, mean = (sum of all observations) / (number of observations). It is affected by extreme values.
Median is the middle value when data is arranged in order. For n observations: if n is odd, median = ((n+1)/2)th term; if even, average of (n/2)th and (n/2+1)th terms.
Mode is the observation that occurs most frequently. A data set can be unimodal, bimodal, or have no mode.
For Class IX, frequency polygons are drawn by joining the midpoints of the tops of histogram bars (including imaginary bars at each end).