📊 CBSE · Class 9 · Mathematics · Chapter 14

Chapter 14
Statistics

Complete chapter resources for CBSE Class 9 Maths — frequency distributions, measures of central tendency (mean, median, mode), bar graphs, histograms, and frequency polygons, with sample questions and board tips.

3Topics
4–6Board marks
8Sample questions
3PYQ included
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Key Formulas — Chapter 14
  • Mean (ungrouped): x̄ = Σxᵢ / n
  • Median (odd n): M = ((n+1)/2)th value
  • Median (even n): M = [(n/2)th + (n/2+1)th] / 2
  • Mode: most frequently occurring value
  • Class mark: (lower limit + upper limit) / 2
  • Range: largest value − smallest value
Chapter Overview

What this chapter covers

Statistics is the branch of mathematics concerned with collecting, organising, presenting, and interpreting numerical data. Chapter 14 of NCERT Class 9 Mathematics introduces students to the foundational ideas of data handling: the distinction between primary and secondary data, constructing frequency distribution tables for both ungrouped and grouped data, and choosing appropriate class intervals to summarise large datasets meaningfully.

The chapter covers three essential measures of central tendency — mean, median, and mode — for ungrouped data. The mean is computed as the sum of all observations divided by the total count. The median is the middle value when data is arranged in order, and the mode is the most frequently occurring value. Students learn when each measure is most appropriate and how to interpret them in context. These concepts are the statistical vocabulary that underpins data-driven reasoning across all subjects.

The chapter also develops graphical literacy: students construct and interpret bar graphs for discrete data, histograms for continuous grouped data, and frequency polygons by joining midpoints of histogram bars. Board questions routinely ask students to draw one of these graphs from a given frequency table, calculate the mean of a dataset, or find the median — skills that are directly assessed in 4–6 marks across the annual examination.

Topics

What's inside Chapter 14

As per NCERT Class 9 Mathematics (CBSE syllabus)

Topic 1
Collection & Organisation of Data
Primary vs. secondary data. Frequency distribution tables — ungrouped (tally marks) and grouped (class intervals, class width, class mark). Choosing appropriate class size for large datasets.
Topic 2
Graphical Representation of Data
Bar graphs for discrete/categorical data. Histograms for continuous grouped data (no gaps between bars). Frequency polygons — plotting midpoints of class intervals and joining them. Reading and interpreting all three graph types.
Topic 3
Measures of Central Tendency
Mean: arithmetic average (Σxᵢ/n). Median: middle value for odd n; average of two middle values for even n — data must be sorted first. Mode: most frequent observation. When to use each measure and their real-world interpretation.
Connections

How this chapter fits in

Useful for setting question difficulty and cross-chapter papers.

Builds on
Class 8 · Data Handling
Bar graphs, pie charts, frequency tables from Class 8 NCERT
Ch 1 · Number Systems
Real-number arithmetic used in computing mean and median
Chapter 14 Statistics
Leads to
Class 10 · Statistics
Grouped data mean (direct, assumed mean), ogive, cumulative frequency
Class 11 · Statistics & Probability
Variance, standard deviation, probability distributions
Board Blueprint

Marks & question-type breakdown

Typical pattern based on CBSE Class 9 Maths annual exam papers from the last five years.

Question type Marks Typical count What's usually tested
MCQ / Objective 1 1 Identify mean/median/mode from a small dataset, or read a histogram value
Very Short Answer 2 1 Calculate mean or median for ungrouped data, or find class mark
Short Answer 3 1 Construct a frequency distribution table or find median for a larger dataset
Long Answer / Graph 4–5 0–1 Draw a histogram or frequency polygon from a given frequency table
Total (approximate) 4–6 3–4 Weightage varies across paper sets and years
Sample Questions

8 sample questions — generated by MarksZen AI

Aligned to CBSE Class 9 Maths Chapter 14. Covers all question types across Easy, Medium, and Hard difficulty.

Q1 Easy 1 mark MCQ
The mode of the data set 3, 5, 7, 5, 3, 5, 8, 3, 5 is: (a) 3 (b) 5 (c) 7 (d) 8
Q2 Easy 2 marks Short Answer
Find the mean of the following data: 12, 18, 24, 30, 36, 42, 48
Q3 Medium 2 marks Short Answer
Find the median of the following observations arranged in ascending order: 8, 14, 20, 25, 31, 37, 44, 50 (Note: n is even — apply the appropriate formula.)
Q4 Medium 3 marks Short Answer
The marks obtained by 15 students in a class test are: 45, 52, 38, 61, 74, 52, 48, 61, 52, 39, 74, 61, 55, 38, 61 Find the (i) mean, (ii) mode, and (iii) median of the data.
Q5 Medium 3 marks Word Problem
The mean of 10 observations is 24. If one observation 30 is replaced by 50, what is the new mean? Show your working clearly.
Q6 Hard 4 marks Short Answer
The following data gives the number of students in different age groups in a school: Age (years): 5–8 | 8–11 | 11–14 | 14–17 | 17–20 No. of students: 20 | 35 | 55 | 40 | 15 (i) Construct a frequency distribution table with class marks. (ii) Calculate the mean age using the class marks.
Q7 Hard 4 marks Word Problem
The mean of 6 numbers is 32. The mean of the first four numbers is 28 and the mean of the last three numbers is 36. (i) Find the sum of all 6 numbers. (ii) Find the fourth number (the one that is counted in both groups).
Q8 Hard 5 marks Graph Question
The weekly pocket money (in ₹) of 30 students is recorded below: Pocket money (₹): 0–50 | 50–100 | 100–150 | 150–200 | 200–250 No. of students: 4 | 8 | 10 | 6 | 2 (i) Draw a histogram for the above data. (ii) Draw a frequency polygon on the same graph. (iii) Find the class with the highest frequency and state its class mark.
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Previous Year Questions

From CBSE board examinations

Actual questions from past Class 9 Maths board and annual exam papers — Statistics chapter.

Board 20223 marks
The mean of 5 numbers is 18. If one number is excluded, the mean of the remaining 4 numbers becomes 16. Find the excluded number. (CBSE Annual 2022)
Board 20234 marks
Following is the data of daily wages (in ₹) of 20 workers in a factory: 250, 310, 290, 340, 270, 310, 295, 250, 310, 280, 340, 310, 260, 295, 310, 270, 250, 340, 295, 310. Prepare a frequency distribution table for this data and find the mode. (CBSE Annual 2023)
Board 20205 marks
The heights (in cm) of 50 students of a class are given in the following frequency distribution table: Height (cm): 130–140 | 140–150 | 150–160 | 160–170 | 170–180 No. of students: 5 | 11 | 20 | 9 | 5 Draw a histogram and frequency polygon for the above data. (CBSE Annual 2020)
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FAQ

Questions teachers ask

How many marks does Statistics carry in the CBSE Class 9 Mathematics exam? +
Statistics typically carries 4–6 marks in the CBSE Class 9 Maths annual exam — usually one 2-mark question on measures of central tendency and one 3-mark question involving frequency distribution or graphical representation. The exact weightage may vary by school and paper set, but this chapter appears consistently in every year-end assessment.
What is the difference between mean, median, and mode in Class 9 Statistics? +
Mean is the arithmetic average of all observations (sum of all values divided by the count). Median is the middle value when data is arranged in ascending or descending order — for an even number of observations it is the average of the two middle values. Mode is the value that appears most frequently in the dataset. All three are measures of central tendency, but they differ in what aspect of the data they represent.
What is the difference between a bar graph and a histogram in Class 9? +
A bar graph represents discrete (ungrouped) data with gaps between bars — each bar corresponds to a distinct category or value. A histogram represents continuous (grouped) data as a frequency distribution with no gaps between bars — the width of each bar equals the class width and the height equals the frequency. Bar graphs are used for qualitative or discrete data; histograms are used for continuous quantitative data grouped into class intervals.
How do you find the median for an even number of observations? +
Arrange all observations in ascending order. For n observations where n is even, the median is the average of the (n/2)th and the (n/2 + 1)th values. For example, if you have 10 observations, the median is (5th value + 6th value) / 2. Always ensure the data is sorted before applying this formula.
How do I generate a custom question paper for Statistics (Class 9) using MarksZen? +
Sign up for a free MarksZen account, choose CBSE Class 9 Mathematics, select Chapter 14 (Statistics), set your preferred question-type mix (MCQ, short answer, graph questions) and total marks — the AI generates a complete board-aligned paper with answer key in under 2 minutes, ready for PDF export.