L-05, Ch-12th, Statistics, NCERT Ex. 12.1 Q1-4,

📘 Class 9 Maths Chapter 12 – Statistics | Full Chapter Summary

In this chapter, "Statistics", we learn how to collect, organize, and represent data in a meaningful way and how to find measures of central tendency such as mean, median, and mode. These tools help us interpret data easily in day-to-day life and real-world applications like surveys, reports, and experiments.
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🔹 1. What is Statistics?
Statistics is the branch of mathematics that deals with the collection, organization, presentation, analysis, and interpretation of data.


🔹 2. Important Terms

Data →
Collection of information (numerical or categorical).

Raw Data →
Unorganized data collected from observation or experiment.

Arrayed Data →
Data arranged in ascending or descending order.

Frequency →
The number of times an observation occurs.

Frequency Distribution Table →
A table showing the values of observations and their corresponding frequencies.

Class Interval →
The range into which data is grouped (e.g., 0–10, 10–20, etc.).

Class Size (h) →
The difference between upper and lower class limits.


🔹 3. Types of Frequency Distribution
Ungrouped Frequency Distribution → Used for small data sets.
Grouped Frequency Distribution → Used when data is large, divided into classes.


🔹 4. Graphical Representation of Data
Visual representation makes understanding easier.

Bar Graph → Rectangular bars of equal width representing frequencies.

Histogram → Bars without gaps used for continuous data.

Frequency Polygon → Formed by joining midpoints of histogram bars.

Ogive (Cumulative Frequency Curve) → Represents cumulative frequency data (introduced in higher classes).


🔹 6. Comparison of Mean, Median & Mode

Mean
Arithmetic average
For numerical, evenly distributed data

Median
Middle value
When data has extreme values or outliers

Mode
Most frequent value
When data is categorical or repetitive


🎯 Key Learning Outcomes

Understanding data handling and frequency distributions.

Representing data graphically using bar graphs, histograms, and polygons.

Calculating and comparing mean, median, and mode.

Developing analytical skills to interpret data effectively.

Laying the foundation for advanced statistics in Class 10 & higher studies.


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