CBSE • Class 9 • Mathematics • Chapter 12 (Statistics) • Exercise 14.1

Exercise 14.1: Statistics — NCERT Solutions

Presenting raw data — tally marks, frequency tables and graphical displays.

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What this exercise covers

Frequency tableBar graph vs histogramClass intervals

Step-by-step solutions — Exercise 14.1

6 solved questions • Each solution includes a Socratic hint, full working and a common-mistake callout • Last reviewed 2026-09-03

Exercise 14.1 Q1 • 3 marks

The number of children in 20 families of a locality are recorded as: 2, 1, 3, 2, 0, 1, 2, 3, 4, 2, 1, 2, 0, 3, 2, 1, 2, 4, 3, 2. Represent this data using a frequency distribution table with tally marks.
Hint (Socratic — try this first)▾
How can you group repeated values and record each occurrence one stroke at a time?
Step-by-step solution▾

Count how many times each value appears using tally marks (bundle every fifth stroke).

| Number of children | Tally marks | Frequency | |:---:|:---:|:---:| | 0 | ll | 2 | | 1 | llll | 4 | | 2 | llll lll | 8 | | 3 | llll | 4 | | 4 | ll | 2 | | Total | | 20 |

All frequencies add up to 2+4+8+4+2=202+4+8+4+2 = 20, which equals the number of families, confirming the table is complete.

Common mistake:
Forgetting to check that the frequencies total 20, or miscounting the value 2 which occurs most often.
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Exercise 14.1 Q2 • 4 marks

The marks (out of 50) scored by 30 students in a test are given below. Construct a grouped frequency distribution table with class intervals 0–10, 10–20, 20–30, 30–40, 40–50: 12, 23, 34, 45, 9, 18, 27, 36, 41, 5, 15, 25, 33, 47, 22, 38, 29, 11, 44, 30, 8, 19, 26, 40, 35, 21, 13, 48, 31, 24.
Hint (Socratic — try this first)▾
In the class 20–30, which endpoint is included and which is excluded?
Step-by-step solution▾

Use the exclusive (continuous) method: a value equal to the upper limit goes into the next class. So 3030 belongs to 3030–4040, not 2020–3030.

| Class interval | Tally | Frequency | |:---:|:---:|:---:| | 0–10 | lll | 3 | | 10–20 | llll l | 6 | | 20–30 | llll lll | 8 | | 30–40 | llll ll | 7 | | 40–50 | llll l | 6 | | Total | | 30 |

Check: 3+6+8+7+6=303+6+8+7+6 = 30 students. ✓

Common mistake:
Placing a boundary value like 30 into the lower class 20–30 instead of the upper class 30–40, breaking the exclusive convention.
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Exercise 14.1 Q3 • 3 marks

The blood groups of 25 students are: A, B, O, O, AB, A, O, B, A, O, B, AB, O, A, O, B, A, AB, O, A, B, O, A, O, B. Prepare a frequency table and state which blood group is the most common.
Hint (Socratic — try this first)▾
Which category shows the highest tally count?
Step-by-step solution▾

Tally each blood group:

| Blood group | Tally | Frequency | |:---:|:---:|:---:| | A | llll ll | 7 | | B | llll l | 6 | | O | llll llll | 9 | | AB | lll | 3 | | Total | | 25 |

Check: 7+6+9+3=257+6+9+3 = 25. ✓

The most common blood group is O, occurring 9 times.

Common mistake:
Miscounting one category so the total does not equal 25, or confusing frequency with the alphabetical order of groups.
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Exercise 14.1 Q4 • 4 marks

The daily wages (in ₹) of 40 workers are grouped into the classes 200–250, 250–300, 300–350, 350–400 with frequencies 8, 14, 12 and 6 respectively. Draw a bar graph representation and find how many workers earn less than ₹300.
Hint (Socratic — try this first)▾
Which two classes together cover all wages below ₹300?
Step-by-step solution▾

Frequency table:

| Wage (₹) | Frequency | |:---:|:---:| | 200–250 | 8 | | 250–300 | 14 | | 300–350 | 12 | | 350–400 | 6 |

Bar graph: On the x-axis mark the wage classes and on the y-axis mark frequency (scale: 1 unit = 2 workers). Draw bars of heights 8, 14, 12 and 6 of equal width with equal gaps between them.

Workers earning less than ₹300 = classes 200–250 and 250–300: 8+14=22 workers.8 + 14 = 22 \text{ workers}.

Common mistake:
Drawing bars of unequal width or leaving unequal gaps; also including the 300–350 class when counting 'less than ₹300'.
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Exercise 14.1 Q5 • 3 marks

The number of hours spent on homework by 15 students in a day are: 1, 2, 2, 3, 1, 4, 2, 3, 2, 1, 4, 3, 2, 1, 3. Draw a bar graph and state the range of the data.
Hint (Socratic — try this first)▾
Range compares the largest and smallest values — what are they here?
Step-by-step solution▾

Frequency table:

| Hours | Frequency | |:---:|:---:| | 1 | 4 | | 2 | 5 | | 3 | 4 | | 4 | 2 |

Check: 4+5+4+2=154+5+4+2 = 15. ✓

Bar graph: x-axis = number of hours (1, 2, 3, 4), y-axis = frequency (scale 1 unit = 1 student). Bars of heights 4, 5, 4, 2 of equal width with equal spacing.

Range = maximum value − minimum value =4−1=3= 4 - 1 = 3 hours.

Common mistake:
Confusing range with the highest frequency; range uses the data values themselves, not their counts.
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Exercise 14.1 Q6 • 3 marks

A survey of favourite sports of 50 students gave: Cricket 18, Football 12, Hockey 8, Badminton 7, Tennis 5. Represent this data by a bar graph and find the fraction of students who prefer Cricket.
Hint (Socratic — try this first)▾
A fraction compares one category's frequency to the total — what is the total?
Step-by-step solution▾

Bar graph: x-axis = sports, y-axis = number of students (scale 1 unit = 2 students). Draw bars of equal width and equal gaps with heights 18, 12, 8, 7, 5.

Total students =18+12+8+7+5=50= 18+12+8+7+5 = 50. ✓

Fraction preferring Cricket: 1850=925.\frac{18}{50} = \frac{9}{25}.

Common mistake:
Not simplifying the fraction or using the wrong total (forgetting to add all five categories).
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How to approach Exercise 14.1

  1. Re-read the chapter summary first. Open Statistics and refresh the key concepts: Frequency distribution, Class interval, Histogram, Frequency polygon.
  2. Try each problem yourself before opening the solution. Ten focused minutes per problem usually beats reading two finished solutions.
  3. Use Guru AI for the questions you get stuck on. The Socratic AI tutor walks you through it with hints instead of dictating the answer.
  4. Mark the questions you got wrong and revisit them after 24 hours — the spacing is what locks the method into long-term memory.

All exercises in Statistics

  1. Exercise 14.1 — Presenting raw data — tally marks, frequency tables and graphical displays.
  2. Exercise 14.2 — Mean of ungrouped data and interpreting diagrams built from grouped-looking tables.

Exercise 14.2 →

Mean of ungrouped data and interpreting diagrams built from grouped-looking tables.

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