Statistics

Why This Chapter Matters

Statistics begins when a list of numbers becomes too large to understand by inspection. Organising data reveals patterns: what is typical, what is common and how one group compares with another.

Class 9 develops the language of data—observations, frequency, grouped distributions and graphical displays—and revisits mean, median and mode with more interpretation.

The goal is not only to calculate. A statistically correct number can still be misleading if the data are poorly organised or the wrong measure is chosen. Every calculation should therefore be followed by the question: what does this result actually tell us?

Bridge from Earlier Classes

Before starting, be comfortable with:

• Tables
• Bar graphs
• Arithmetic average
• Ordering numbers
• Basic percentage sense

These are the tools this chapter reuses and deepens.

1. Raw Data and Frequency

Raw data are observations in the form originally collected. A frequency table counts how many times each value occurs.

Frequency organisation reduces clutter and reveals repeated patterns. The total of all frequencies must equal the total number of observations because every observation must be counted exactly once.

2. Grouped Frequency Distribution

When values cover a wide range, individual frequencies may still be inconvenient. Grouping observations into class intervals creates a compact summary.

Intervals should be systematic and non-overlapping. Exclusive intervals such as 10–20, 20–30 and 30–40 make boundary placement clear for continuous-style data.

3. Class Marks

The class mark is the midpoint of an interval. It provides a representative central value for that class.

For class 20–30, the class mark is (20+30)/2 = 25. Class marks become useful when grouped data are plotted or later summarised numerically.

4. Histogram

A histogram represents continuous grouped data using adjacent rectangles.

Unlike an ordinary bar graph, the bars touch because the class intervals lie on a continuous number scale. The horizontal axis shows class intervals and the vertical axis shows frequency.

5. Frequency Polygon

A frequency polygon plots class marks against frequencies and joins the points by straight segments.

It can be drawn over a histogram or independently. Its advantage is that the overall shape of a distribution is visible quickly, and two distributions can be compared more easily than with bulky bars.

6. Mean

The arithmetic mean is the total of all observations divided by the number of observations.

Because every value contributes, the mean is sensitive to extreme observations. This can be useful when extremes matter, but it can also make the mean less representative of a typical value.

7. Median and Mode

The median is the middle value after arranging data in order. For an even number of observations, it is the average of the two middle values.

The mode is the most frequently occurring value. Median is often resistant to extreme values, while mode is useful when the most common value or category is the main interest.

8. Choosing the Right Average

Suppose most salaries are near ₹20,000 but one salary is ₹2,00,000. The mean rises sharply because of the extreme value, while the median remains closer to what most workers earn.

So 'average' is not one universal idea. The correct measure depends on the question and the shape of the data.

Visualise the Core Idea

Histograms show grouped frequencies; frequency polygons show the distribution through connected midpoint values.

Formula / Theorem Sheet

Worked Examples — Follow the Reasoning

How to Think in the Exam

Common Mistakes

Quick Revision

Focused Practice

Final Chapter Summary