Statistics

Class 9 Maths • Chapter 12 • Comprehensive Guide

1. Collection of Data

Statistics deals with the collection, organization, analysis, and interpretation of data.

Primary Data

Click to see definition & example

Definition

Data collected by the investigator herself/himself with a specific purpose in mind.

Ex: Measuring heights of students in your class.

Secondary Data

Click to see definition & example

Definition

Data gathered from a source which already had the information stored.

Ex: Cricket scores from a website.

2. Frequency Distribution

Frequency is the number of times a particular entry occurs. We use Tally Marks to count.

Tally Mark Transformer

Enter a number (1-20) to see it in Tally Marks.

2.1 Grouped Data & Class Intervals

When data is large, we condense it into groups called Class Intervals (e.g., 0-10, 10-20).

Upper Limit: The higher value of a class (e.g., 10 in 0-10).
Lower Limit: The lower value (e.g., 0 in 0-10).
Class Size (Width): Upper Limit - Lower Limit.
Class Mark: The mid-point of a class. Formula: \( \frac{\text{Upper Limit} + \text{Lower Limit}}{2} \)

Class Mark Calculator

Find the midpoint of a class interval.

3. Graphical Representation

Data visualization is key. We focus on:

Bar Graphs: Bars of uniform width with equal spacing (gaps) for distinct categories.
Histograms: Adjacent bars (no gaps) over continuous class intervals. Area represents frequency.
Frequency Polygons: Joining the mid-points (Class Marks) of the upper sides of the adjacent bars of a histogram.

Graph Builder

Toggle between Bar Graph (Discrete) and Histogram (Continuous).

Mode: Bar Graph

Unequal Class Histogram (CBSE Special)

When class widths are different, use:
Adjusted Frequency = (Frequency × Smallest Class Width) / Class Width

Class Interval	Frequency	Width	Adjusted Frequency
0–10	5	10	5
10–30	9	20	4.5

✔ Use adjusted frequencies for drawing histogram

3.1 Frequency Polygon

A frequency polygon is obtained by joining the mid-points (class marks) of histogram bars.

Frequency Polygon Builder

✔ Always start and end polygon on X-axis

3.2 Ogive (Cumulative Frequency Curve)

An Ogive represents cumulative frequencies.

Less than Ogive: Uses upper class limits
More than Ogive: Uses lower class limits

✔ Ogives help locate median graphically (Class 10 preview)

📌 CBSE Exam Rules (Must Remember)

Bar Graph: Used for discrete data, equal gaps between bars.
Histogram: Used for continuous data, no gaps between bars.
Histogram Area ∝ Frequency (not height alone).
Unequal Class Intervals: Histogram must be adjusted using frequency density.

How to Draw Graphs in Board Exam ✍️

Draw X and Y axes neatly using pencil.
Choose suitable scale (write scale).
Mark class intervals on X-axis.
Mark frequencies on Y-axis.
Draw bars (with or without gaps as required).
Label graph and give title.

✔ Always use pencil, ruler, and scale

Common Mistakes ❌

❌ Drawing gaps in histogram
❌ Not adjusting unequal class widths
❌ Forgetting scale on axes
❌ Mixing bar graph & histogram rules

4. Measures of Central Tendency

Measure	Description	Formula
Mean (\(\bar{x}\))	Average of all observations.	Raw: \( \frac{\sum x_i}{n} \) Grouped: \( \frac{\sum f_i x_i}{\sum f_i} \)
Median	Middle value when sorted.	\(\frac{n+1}{2}\)th (Odd) / Avg of mid two (Even)
Mode	Most frequent observation.	Max Frequency

Stats Command Center

Enter numbers separated by commas (e.g., 5, 2, 8, 2, 10).

Concept Mastery Quiz

1. The class mark of the interval 10 - 25 is:

2. In a histogram, the area of each rectangle is proportional to:

3. The mode of the data: 2, 3, 4, 2, 12, 2, 7 is:

4. Histograms are used for ______ data.

5. To find the median, data must first be: