Vardaan
Class 9 Maths Ӣ Chapter 12 Ӣ NCERT Core

Statistics

Vardaan Learning Institute  |  Data Handling & Visualisation

Syllabus Update Note In the latest rationalised NCERT syllabus, Mean, Median, and Mode of ungrouped data have been removed from Class 9. The focus is entirely on Graphical Representation of Data (Bar Graphs, Histograms, Frequency Polygons).

📊 1. Collection & Presentation of Data

Ӣ Data: Facts or figures collected with a definite purpose.
Ӣ Primary Data: Data collected by the investigator themself directly (e.g., measuring height of classmates).
Ӣ Secondary Data: Data collected by someone else / from existing sources (e.g., taking temperature data from newspaper).

Frequency Distribution Table

We present data in tables to make it meaningful. For large data, we use Grouped Frequency Distribution.

Continuous vs Discontinuous Data:
If classes are 11-20, 21-30, 31-40 (Discontinuous).
We must make it continuous to draw a histogram. Subtract 0.5 from lower limit, add 0.5 to upper limit.
New classes: 10.5-20.5, 20.5-30.5, 30.5-40.5.

📈 2. Graphical Representation of Data

1. Bar Graph
A B C

Ӣ Used for discrete/categorical data.
Ӣ Bars have equal width.
Ӣ Equal gap between all bars.

2. Histogram
10 20 30

Ӣ Used for continuous grouped data.
Ӣ NO gap between bars.
Ӣ Area of bar is proportional to frequency.
Ӣ Kink (zig-zag) used if x-axis doesn't start from 0.

3. Frequency Polygon

A frequency polygon is constructed by plotting the frequencies against the class marks and joining the points with straight lines.

Start & End on X-axis
1. Find the Class Marks of all classes.
2. Take the preceding class and succeeding class (both with frequency 0) to "close" the polygon on the x-axis.
3. A frequency polygon can be drawn independently without drawing a histogram first by just using class marks.

⚠️ Adjusting Frequencies for Unequal Class Widths

If drawing a histogram and the class sizes are NOT equal, you MUST adjust the frequencies to maintain the proportional area.
Adjusted Frequency = $\frac{\text{Minimum Class Size}}{\text{Class Size of this class}} \times \text{Frequency}$
✏️ Practice Questions — Statistics (22 Questions)

Section A — 1 Mark Conceptual Easy

Q1. What is the class mark of the interval 150-160?
Q2. Range of data: 25, 18, 20, 22, 16, 6, 17, 15, 12, 30.
Q3. In a histogram, the area of each rectangle is proportional to ________.
Q4. True/False: In a bar graph, bars can be drawn horizontally or vertically.
Q5. What is the class size of the interval 30.5 - 35.5?
Q6. If class marks are 15, 20, 25, 30... find the class corresponding to class mark 20.
Q7. Which graph is used for continuous data?
Q8. Convert the discontinuous classes 1-10, 11-20 into continuous classes.

Section B — Graphical Drawing Skills Medium

*(Questions to practice on graph paper)*

  1. Q9. A family with a monthly income of ₹20,000 had planned the following expenditures: Grocery (4k), Rent (5k), Education (5k), Medicine (2k), Fuel (2k), Misc (2k). Draw a Bar Graph.
  2. Q10. The daily routine of a student is: Sleep 8h, School 6h, Play 2h, TV 2h, Study 4h, Misc 2h. Represent via a Bar Graph.
  3. Q11. Given the continuous grouped data of weights of 38 students: 31-35 (9), 36-40 (14), 41-45 (11), 46-50 (2), 51-55 (2). Make it continuous (30.5-35.5 etc.) and draw a Histogram.
  4. Q12. Draw a Frequency Polygon for the marks: 0-10 (5), 10-20 (10), 20-30 (15), 30-40 (20), 40-50 (12), 50-60 (8). (Draw it over a Histogram).
  5. Q13. Draw a Frequency Polygon for Q12 without drawing a Histogram (Use class marks).

Section C — NCERT High-Weightage (Adjusted Freq) Hard

  1. Q14. 100 surnames were randomly picked. Letter frequency: 1-4 (6), 4-6 (30), 6-8 (44), 8-12 (16), 12-20 (4). Draw a Histogram. (Hint: Classes are unequal. Adjust frequency. Min class size = 2).
  2. Q15. Ages of 100 passengers in a train: 0-10 (5), 10-20 (15), 20-30 (20), 30-40 (25), 40-50 (15), 50-60 (10), 60-70 (10). Draw a Frequency Polygon.
  3. Q16. For a frequency polygon, what endpoints must be added to the x-axis to close the polygon for the data in Q15?
  4. Q17. A study on cost of living index: 140-150 (5), 150-160 (10), 160-170 (20), 170-180 (9), 180-190 (6), 190-200 (2). Draw a Histogram AND a Frequency Polygon on the same axes.
  5. Q18. Marks of two sections A and B on same graph using Frequency Polygons matching class marks. Compare performance.

Section D — Competency & Conceptual Questions Hard

  1. Q19. Why is a kink ($\sim$) used on the x-axis in a histogram?
  2. Q20. If a frequency distribution has classes 0-5, 5-10, 10-15... where is the observation '10' counted?
  3. Q21. In the adjusted frequency formula for a histogram, if the class size of the interval 20-30 is 10, the class size of 30-50 is 20, and the min class size is 10. If the frequency of 30-50 is 30, what is its modified drawing frequency?
  4. Q22. Can a frequency polygon be drawn without a histogram? If yes, what is plotted on the x-axis?
✅ Key Checkpoints: Q1: $\frac{150+160}{2} = 155$ | Q2: Max(30) - Min(6) = 24 | Q5: Size = Upper-Lower = 5 | Q6: 17.5-22.5 | Q8: 0.5-10.5, 10.5-20.5 | Q14: Modified frequencies for drawing: 3, 30, 44, 8, 1 | Q16: Class Marks -5 and 75 | Q19: To compress the gap between origin (0) and the first class interval if it starts far from 0. | Q20: In the 10-15 class. | Q21: $\frac{10}{20} \times 30 = 15$.