Statistics Class 9 Maths Worksheet with Answers Chapter 12

Chapter 12 is the last chapter of the NCERT maths book. In the worksheet for the last chapter, Surface Areas and Volumes, below, you will find questions with 4 levels: Basic, Standard, Advance, and HOTS. The 4 sections will help you practice from direct graph rules to tricky mixed-data cases. Attempt this worksheet only after you have finished the chapter. First, revise the class marks, continuous intervals, and frequency density before solving these questions. Here are the major sections from the chapter covered –

• Data representation graphs
• Bar graph basics
• Histogram construction steps
• Frequency polygon plotting
• Frequency density concept

Class 9 Maths Worksheet – Chapter 12: Statistics

Note: Attempt after completing the chapter. Use neat tables and show key steps (class-mark, continuous intervals, frequency density).

Basic

1. The number of books read by students in a month is:
   • A: 3
   • B: 5
   • C: 2
   • D: 6
   • E: 4

   Which graph is most suitable: bar graph or histogram? Give one reason.

2. Find the class-mark for each class:
   • 10–20
   • 20–30
   • 30–40
   • 40–50
3. Make the following class intervals continuous (using correction of 0.5):
   • 5–9, 10–14, 15–19, 20–24
4. A frequency table is:
   Marks: 0–10, 10–20, 20–30, 30–40
   Frequency: 4, 7, 6, 3
   Write the ordered pairs (class-mark, frequency) needed to draw a frequency polygon.
5. True/False (write one line reason):
   • In a bar graph, bars touch each other.
   • In a histogram, bars touch each other.
   • Histogram is used for continuous data.
6. The weights (kg) of students are grouped as:
   30.5–35.5: 9, 35.5–40.5: 6, 40.5–45.5: 15
   Which class has the maximum frequency? Also write the class size.

Standard

1. Draw a bar graph for:
   Heads (Monthly spend in ₹000):
   • Food: 6
   • Rent: 8
   • Transport: 3
   • Books: 2
   • Others: 1

   Write:

   • Scale chosen on y-axis
   • Which head is maximum
2. The marks of 36 students are:
   0–10: 3, 10–20: 7, 20–30: 12, 30–40: 8, 40–50: 6
   Write the class-marks and plot points for a frequency polygon (no need to draw, just list points).
3. The lifetimes (hours) of bulbs:
   300–400: 14, 400–500: 56, 500–600: 60, 600–700: 86, 700–800: 74
   How many bulbs have lifetime more than 700 hours?
4. A histogram is to be drawn for:
   118–126: 3, 127–135: 5, 136–144: 9, 145–153: 12
   First make the classes continuous and write the new intervals.
5. For the grouped data:
   10–20: 5, 20–30: 9, 30–40: 7, 40–50: 4
   Find:
   • Total frequency
   • Modal class (highest frequency class)
6. Explain in 2–3 lines:
   Why does a frequency polygon often add one class before the first class and one class after the last class with frequency 0?

Advance

1. A teacher grouped marks as varying classes:
   0–20: 6, 20–40: 14, 40–50: 10, 50–70: 12, 70–100: 8
   Is a simple histogram with heights equal to frequencies correct? If not, what should be used instead of frequency for bar height?
2. For the varying-width classes below, compute the frequency density (frequency ÷ class width):
   • 0–20: 6
   • 20–40: 14
   • 40–50: 10
   • 50–70: 12
   • 70–100: 8
3. The ages (years) of children in a park:
   1–2: 5, 2–3: 3, 3–5: 6, 5–7: 12, 7–10: 9
   Which intervals have width 2 or more? For those, write frequency density.
4. Two sections A and B have marks distribution:
   Class: 0–10, 10–20, 20–30, 30–40, 40–50
   Freq A: 3, 9, 17, 12, 9
   Freq B: 5, 19, 15, 10, 1
   Compute class-marks and list points for both frequency polygons.
5. In a frequency polygon, why do we use class-marks on the x-axis and not class limits?
   Write a 2-line explanation.
6. A histogram shows the highest rectangle for class 40–50.
   Give two correct conclusions and one incorrect conclusion students often make.

HOTS

1. A student draws a histogram for:
   0–20: 7, 20–30: 10, 30–40: 10, 40–50: 20, 50–60: 20, 60–70: 15, 70–100: 8
   and says: “70–100 has more students than 60–70 because its bar looks taller.”
   Explain the mistake in 3–4 lines.
2. For the table:
   0–20: 7, 20–30: 10, 30–40: 10, 40–50: 20, 50–60: 20, 60–70: 15, 70–100: 8
   Take minimum class size = 10 and compute the adjusted heights (proportional to width 10) for:
   • 0–20
   • 70–100
3. Two teams A and B scored runs in 10 equal class-intervals of balls:
   1–6: A=2, B=5; 7–12: A=1, B=6; 13–18: A=8, B=2; 19–24: A=9, B=10
   Which team is more consistent in these four intervals? Give one statistical reason based on variation.
4. If two different histograms are drawn for the same data using different scales, can the conclusion about “maximum frequency class” change?
   Answer Yes/No with reason.
5. A data set has continuous classes. A student uses a bar graph instead of a histogram.
   What visual error might occur? Explain in 2–3 lines.
6. Create one real-life situation where a frequency polygon is better than a histogram for comparison.
   (Example: two classes, two hospitals, two years etc.) Write 2–3 lines.

Answer Key

Basic – Answers

1. Ans: Bar graph.
   Hint: Data is discrete categories (students A–E), not continuous class intervals.
2. Ans:
   • 10–20 → 15
   • 20–30 → 25
   • 30–40 → 35
   • 40–50 → 45

   Hint: Class-mark = (lower + upper)/2.

3. Ans: 4.5–9.5, 9.5–14.5, 14.5–19.5, 19.5–24.5
   Hint: Subtract 0.5 from each lower limit and add 0.5 to each upper limit.
4. Ans: Class-marks: 5, 15, 25, 35
   Points: (5,4), (15,7), (25,6), (35,3)
   Hint: Use class-marks on x-axis.
5. Ans:
   • Bar graph bars touch: False (gaps are there)
   • Histogram bars touch: True
   • Histogram for continuous: True

   Hint: Histogram represents continuous classes so no gaps.

6. Ans: Maximum frequency class is 40.5–45.5 (frequency 15). Class size = 5 kg.
   Hint: Class size = upper − lower.

Standard – Answers

1. Ans: Any correct bar graph with equal bar widths and equal gaps.
   Example scale: 1 unit = ₹1,000.
   Maximum head: Rent (8).
   Hint: y-axis must cover maximum value 8.
2. Ans: Class-marks: 5, 15, 25, 35, 45
   Points: (5,3), (15,7), (25,12), (35,8), (45,6)
   Hint: List points; joining gives polygon.
3. Ans: More than 700 hours = 700–800 + 800–900 + 900–1000
   Given here only up to 700–800: 74
   So from given table: 74
   Hint: Add frequencies of classes strictly above 700.
4. Ans: Continuous classes:
   117.5–126.5, 126.5–135.5, 135.5–144.5, 144.5–153.5
   Hint: Use ±0.5 because data is to nearest mm.
5. Ans: Total frequency = 5+9+7+4 = 25
   Modal class = 20–30 (highest frequency 9)
   Hint: Modal class means maximum frequency class.
6. Ans: Extra zero-frequency classes close the polygon to the x-axis and make comparison/area interpretation fair.
   Hint: Polygon should start and end on x-axis.

Advance – Answers

1. Ans: Not correct.
   Use: Frequency density (or adjusted heights proportional to a standard width).
   Hint: In varying widths, rectangle area must match frequency.
2. Ans: Widths: 20, 20, 10, 20, 30
   • 0–20: 6/20 = 0.30
   • 20–40: 14/20 = 0.70
   • 40–50: 10/10 = 1.00
   • 50–70: 12/20 = 0.60
   • 70–100: 8/30 ≈ 0.27

   Hint: Density = frequency ÷ class width.

3. Ans: Widths:
   • 3–5 width 2 ⇒ density = 6/2 = 3
   • 5–7 width 2 ⇒ density = 12/2 = 6
   • 7–10 width 3 ⇒ density = 9/3 = 3

   Hint: Identify width ≥ 2 then compute density.

4. Ans: Class-marks: 5, 15, 25, 35, 45
   Section A points: (5,3), (15,9), (25,17), (35,12), (45,9)
   Section B points: (5,5), (15,19), (25,15), (35,10), (45,1)
   Hint: Same x-values, different y-values.
5. Ans: Class-mark represents the center of each class and gives one clear x-position per class.
   Using limits would give two x-values per class and confuse the polygon.
   Hint: Polygon connects midpoints, not boundaries.
6. Ans (sample):
   • Correct: 40–50 has highest frequency.
   • Correct: Most observations lie near 40–60.
   • Incorrect: “All values are exactly 45.”

   Hint: Grouped data gives ranges, not exact values.

HOTS – Answers

1. Ans: In varying class widths, bar height cannot be raw frequency.
   Histogram compares areas, not just heights.
   A wider class (70–100) can look larger even with smaller frequency.
   Hint: Use frequency density or adjusted heights.
2. Ans:
   • 0–20 (width 20): adjusted height = (7/20)×10 = 3.5
   • 70–100 (width 30): adjusted height = (8/30)×10 ≈ 2.67

   Hint: Adjust to standard width 10.

3. Ans (sample): Team A is more consistent.
   Reason: A’s scores vary less (2,1,8,9) vs B’s (5,6,2,10) which swings more.
   Hint: Consistency means smaller variation.
4. Ans: No.
   Reason: Changing scale changes bar height appearance but not which class has maximum frequency.
   Hint: Ordering by frequency remains same.
5. Ans: Bar graph leaves gaps, which wrongly suggests breaks in continuous data.
   Histogram must show continuous distribution without gaps.
   Hint: Continuous data → continuous bars.
6. Ans (example): Compare marks distribution of Section A and Section B in one test.
   Frequency polygons on the same axes show which section has more students in each class interval clearly.
   Hint: Polygon is great for comparing two distributions.

Worksheet for Other Class 9 Maths Chapters

• Number Systems Class 9 Maths Worksheet Chapter 1
• Polynomials Class 9 Maths Worksheet Chapter 2
• Linear Equations in Two Variables Class 9 Maths Worksheet Chapter 4
• Introduction to Euclid’s Geometry Class 9 Maths Worksheet Chapter 5
• Heron’s Formula Class 9 Maths Worksheet Chapter 10
• Surface Areas and Volumes Class 9 Maths Worksheet Chapter 11