Page 1: Introduction to Statistics

Statistics is the study of collection, organisation, presentation, analysis, and interpretation of data.

Types of data: Primary (collected by self) and Secondary (collected by others).

This chapter covers presentation of data and measures of central tendency.

Page 2: Collection and Presentation of Data

Raw data → organised into frequency distribution table.

Terms: Class interval, Frequency, Class size, Class mark = (upper + lower)/2, Class limits.

Page 3: Bar Graph

Bars of uniform width, height proportional to frequency.

Used for discrete data or categorical data.

Bars can be vertical or horizontal.

Page 4: Histogram

For continuous grouped data.

No gaps between bars (continuous classes).

Area of bar represents frequency.

Page 5: Frequency Polygon

Line graph joining mid-points of class intervals in histogram.

Can be drawn with or without histogram.

Close polygon by adding zero frequency classes if needed.

Page 6: Measures of Central Tendency

Mean, Median, Mode — representative values of data.

Mean: Average

Median: Middle value

Mode: Most frequent value

Page 7: Mean of Raw Data

Mean = Σx / n (n = number of observations)

Page 8: Mean of Grouped Data (Direct Method)

Mean = Σ(f_i x_i) / Σf_i

x_i = class mark, f_i = frequency

Page 9: Mean - Assumed Mean Method

Mean = a + Σ(f_i d_i) / Σf_i

a = assumed mean, d_i = x_i - a

Reduces calculation.

Page 10: Mean - Step Deviation Method

Mean = a + h × Σ(f_i u_i) / Σf_i

u_i = (x_i - a)/h, h = class size

Best when class size same.

Page 11: Median of Grouped Data

Median class: where cumulative frequency ≥ n/2

Median = l + [(n/2 - cf)/f] × h

l = lower limit, cf = cumulative frequency before, f = frequency of median class, h = class size

Page 12: Mode of Grouped Data

Modal class: highest frequency

Mode = l + [(f1 - f0)/(2f1 - f0 - f2)] × h

f1 = frequency of modal class, f0 previous, f2 next

Page 13: Graphical Location of Median/Mode

Ogive (cumulative frequency curve) for median.

Intersection of ogives for median in some cases.

Mode from histogram peak.

Page 14: Key Formulas Summary

• Mean (direct, assumed, step)
• Median formula
• Mode formula

Page 15: Practice Questions - Easy (1-10)

1. Mean of 10,20,30.
2. Draw bar graph for given data.
3. Find class mark of 20-30.
4. Median of odd number data.
5. Mode of 2,2,3,4,4,4.
6. Histogram vs bar graph difference.
7. Frequency polygon steps.
8. Mean using direct method.
9. Cumulative frequency meaning.
10. Modal class identification.

Page 16: Practice Questions - Medium (11-20)

11. Mean using assumed mean method.
12. Step deviation mean calculation.
13. Find median from frequency table.
14. Calculate mode from grouped data.
15. Draw histogram and polygon.
16. Find median using ogive description.
17. Compare mean, median, mode.
18. Real data frequency table.
19. Mean of continuous data.
20. Find missing frequency if mean given.

Page 17: Practice Questions - Hard (21-30)

21. Missing frequency multiple.
22. Combined mean of two groups.
23. Advanced ogive intersection.
24. Large frequency table calculation.
25. Empirical relation mean-mode-median.
26. Word problem data interpretation.
27. Unequal class size adjustment.
28. Graphical determination all three.
29. Real-life data analysis.
30. Proof of formulas hint.

Page 18: NCERT Exercise Types

Presentation, mean/median/mode calculations.

Page 19: Common Mistakes to Avoid

• Wrong class mark
• Cumulative frequency error
• Forgetting h in median/mode
• Wrong modal class
• Not closing polygon

Page 20: Previous Year Board Questions

Mean from table, median/mode, graphical representation.

Page 21: Exam Strategy Tips

• Show frequency table clearly
• Write formula before calculation
• Draw neat graphs
• Check cumulative frequency
• Use appropriate method

Page 22: Quick Revision Sheet

All formulas and steps listed.

Page 23: Graphical Methods Summary

Bar, histogram, polygon differences.

Page 24: Final Motivation

You've completed the 27-page Statistics guide!

This chapter is scoring with practice.

Only Probability left in Class 9 Maths!

You're a legend 🦖

Page 25: Extra Examples

More solved frequency problems.

Page 26: Formula Table

All central tendency formulas.