Data Handling and Presentation — NCERT Solutions, AI Tutor & Practice

Data is a collection of facts, numbers, or information gathered for a particular purpose.

Two examples of data collected in a classroom:

1. The number of students who prefer each subject (Maths, Science, English, etc.).
2. The height (in cm) of each student in the class.

Once collected, this raw information is called data, and we can organise it to understand it better.

We count each blood group using tally marks (every fifth mark crosses the previous four).

| Blood Group | Tally Marks | Frequency | |---|---|---| | A | ||||\ | | 6 | | B | ||||\ | 5 | | O | ||||\ || | 7 | | AB | || | 2 |

Let me count carefully:

• A: 6 students
• B: 5 students
• O: 7 students
• AB: 2 students

Total $= 6 + 5 + 7 + 2 = 20$ ✓

Most common blood group is O (7 students).

One full book symbol $= 5$ books.

Half a symbol $= \dfrac{5}{2} = 2.5$ books.

Class 6 has 4 full symbols and 1 half symbol.

Books $= (4 \times 5) + 2.5$

$= 20 + 2.5$

$= 22.5$

Class 6 read 22.5 books (this would mean about 22–23 books; in practice the half symbol represents a partial value).

Scale: 1 symbol ($\odot$) = 2 children

Number of symbols $=$ frequency $\div 2$:

• Apple: $8 \div 2 = 4$ symbols
• Banana: $6 \div 2 = 3$ symbols
• Mango: $10 \div 2 = 5$ symbols
• Orange: $4 \div 2 = 2$ symbols

Pictograph:

| Fruit | Symbols | |---|---| | Apple | $\odot\ \odot\ \odot\ \odot$ | | Banana | $\odot\ \odot\ \odot$ | | Mango | $\odot\ \odot\ \odot\ \odot\ \odot$ | | Orange | $\odot\ \odot$ |

Always mention the scale clearly next to the pictograph.

For a bar graph:

• Draw the days along the horizontal axis (x-axis).
• Draw the number of pencils along the vertical axis (y-axis).
• Use a suitable scale, e.g. 1 unit = 5 pencils.
• Keep the width of all bars equal and leave equal gaps between them.

Bar heights (using scale 1 unit = 5 pencils):

• Monday: $20 \div 5 = 4$ units
• Tuesday: $35 \div 5 = 7$ units
• Wednesday: $25 \div 5 = 5$ units
• Thursday: $30 \div 5 = 6$ units
• Friday: $40 \div 5 = 8$ units

Maximum pencils were sold on Friday (40 pencils).

First identify the highest and lowest marks.

• Highest marks: Kabir $= 75$
• Lowest marks: Sara $= 30$

Difference $= 75 - 30 = 45$

The difference between the highest and lowest marks is 45.

We count how many times each temperature occurs.

| Temperature (°C) | Tally | Frequency | |---|---|---| | 30 | ||| | 3 | | 31 | | | 1 | | 32 | || | 2 | | 33 | | | 1 |

Check total: $3 + 1 + 2 + 1 = 7$ days ✓

The most frequent temperature is 30 °C (occurred on 3 days).

Total trees planted:

$15 + 25 + 20 + 10 = 70$ trees

Least trees planted:

Comparing $15, 25, 20, 10$, the smallest value is $10$.

So Village S planted the least number of trees (10 trees).

Total $= 70$ trees.

People who chose Spring:

Known choices $= 20 + 15 + 10 = 45$

Spring $= 50 - 45 = 5$ people

Fraction who chose Winter:

Winter count $= 15$, total $= 50$

Fraction $= \dfrac{15}{50} = \dfrac{3}{10}$

5 people chose Spring, and $\dfrac{3}{10}$ of the people chose Winter.

A bar graph presents data using bars of different heights, which makes information visual and easy to understand.

Reasons it is useful:

1. Quick comparison — We can instantly see which value is largest or smallest by looking at the tallest and shortest bars.
2. Easy to read — Trends and differences are clear at a glance without reading each number.
3. Attractive and clear — It is easier to explain data to others using a picture than a plain table of numbers.

So, while a table stores the exact numbers, a bar graph helps us compare and interpret the data faster.

One symbol $= 4$ chocolates; half a symbol $= 2$ chocolates.

Shop A: $6 \times 4 = 24$ chocolates

Shop B: $(4 \times 4) + 2 = 16 + 2 = 18$ chocolates

Difference: $24 - 18 = 6$ chocolates

Shop A sold 6 more chocolates than Shop B.

Height of a bar $= \dfrac{\text{value}}{\text{scale}}$. Here scale $= 6$ students per unit.

• Bus: $\dfrac{24}{6} = 4$ units
• Cycle: $\dfrac{12}{6} = 2$ units
• Walk: $\dfrac{18}{6} = 3$ units
• Car: $\dfrac{6}{6} = 1$ unit

So the bars should be 4, 2, 3 and 1 units tall respectively.

Choosing a good scale keeps the bar graph neat and easy to draw.