UBSE • Class 7 • Mathematics • Ch 3

Estimated Time: 45 Mins

Study Progress: In Progress

Data Handling

In Class 7 Mathematics, Chapter 13 "Connecting the Dots..." introduces students to the foundations of Data Handling and Statistics. Grounded in the 2026–27 NCERT Ganita Prakash curriculum, this master material explores statistical questions, measures of central tendency (Mean / Sama-karana, Median, Mode), data spread (Range), double bar graph interpretation, and basic probability and chance.

Take Chapter CBT Test View All Chapters

Overview Core Concepts Summary Self Check Take MCQ Test

🏏 Have You Ever Wondered?

Who is the better cricket batsman?

Batsman A scored $90, 10, 0, 15,$ and $8$ in $5$ matches (Total: $123$ runs). Batsman B scored $35, 30, 28, 32,$ and $30$ (Total: $155$ runs). Batsman A hit the highest single score ($90$), but Batsman B was steady and dependable in every match.

Looking at raw numbers alone causes arguments. But when you calculate their Batting Average (Arithmetic Mean): $$\text{Batsman A} = \frac{123}{5} = \mathbf{24.6}, \quad \text{Batsman B} = \frac{155}{5} = \mathbf{31.0}$$

Data handling is the art of connecting scattered facts to reveal the real story behind the numbers. In ancient India, mathematicians called the mean Sama-karana—the act of leveling uneven piles into equal ground.

Why This Chapter Matters

Before You Begin (Prerequisites)

Tally marks and frequency distribution tables.
Reading simple single bar graphs from earlier grades.
Fractions and decimals for calculating averages.

What You Will Learn (Core Objectives)

Distinguish between statistical questions and non-statistical questions.
Calculate the Range, Arithmetic Mean, Median, and Mode of given datasets.
Select the appropriate measure of central tendency for different situations.
Construct and interpret Double Bar Graphs to compare two related sets of data.
Calculate the theoretical probability of simple chance events ($P(E) = \frac{\text{favorable}}{\text{total}}$).

Chapter Roadmap & Progression

1 1. Statistical Questions & The Rang...

2 2. The Big Three: Arithmetic Mean,...

3 3. Double Bar Graphs & The Concept...

Complete Concept Guide (100% Curriculum Coverage)

1. Statistical Questions & The Range of Data

1. The Intuition

If you ask: "What is the height of Mount Everest?", there is only one fixed factual answer ($8,848.86\text{ m}$). This is NOT a statistical question.

A statistical question is one that anticipates variability in the answers and can only be answered by collecting data from multiple individuals or trials (e.g., "What are the heights of students in Class 7?").

2. Data Spread: The Range

The Range measures how widely the data values are spread out:

$$\mathbf{\text{Range} = \text{Highest Observation} - \text{Lowest Observation}}$$

A small range means the data is tightly clustered; a large range means the data is widely dispersed.

3. Concrete Worked Example

Example: The marks obtained by 7 students in a test are: $23, 35, 48, 12, 45, 30, 48$. Find the range.

Highest Mark: $48$

Lowest Mark: $12$

Range: $48 - 12 = \mathbf{36\text{ marks}}$.

4. Pitfall & Examiner Trap

⚠️ Trap: Confusing Range with Average
The range tells you the distance from the bottom to the top; it does NOT tell you the typical middle score!

5. Why This Matters in Life

Weather reports quote daily temperature range ($\text{Max } 34^\circ\text{C}, \text{Min } 22^\circ\text{C} \implies \text{Range } 12^\circ\text{C}$) to describe climate extremes.

2. The Big Three: Arithmetic Mean, Median, and Mode

1. The Intuition

When you want one single representative number to describe an entire crowd, mathematics provides three different lenses: the Mean (the leveler), the Median (the middle person), and the Mode (the crowd favorite).

2. Definitions and Calculation Rules

1. Arithmetic Mean ($\bar{x}$)

The sum of all values divided by the total number of observations:

$$\mathbf{\text{Mean} = \frac{\text{Sum of all observations}}{\text{Number of observations}}}$$

2. Median (The Middle Value)

Arrange the data in ascending (or descending) order. The median is the exact middle observation.

• If $n$ is odd → Middle value at position $\frac{n + 1}{2}$.

3. Mode (The Most Frequent)

The observation that occurs with the highest frequency (most repeated). A dataset can have one mode, more than one mode (bimodal), or no mode.

3. Concrete Worked Example

Example: Find the Mean, Median, and Mode for: $14, 25, 14, 28, 18, 17, 14$

Mean: $\frac{14 + 25 + 14 + 28 + 18 + 17 + 14}{7} = \frac{130}{7} \approx \mathbf{18.57}$

Median: Arrange in order: $14, 14, 14, \mathbf{17}, 18, 25, 28$. Middle is the 4th item → $\mathbf{17}$.

Mode: $14$ appears 3 times (most frequent) → $\mathbf{14}$.

4. Pitfall & Examiner Trap

⚠️ Trap: Finding Median Without Sorting the Data First
If you pick the middle number from an unsorted list, your answer will be completely wrong! You MUST arrange the numbers from smallest to largest first.

5. Why This Matters in Life

Shoe store owners order stock based on the Mode (the most common shoe size sold), NOT the average shoe size (which could be a non-existent size like 7.34!).

3. Double Bar Graphs & The Concept of Probability

1. Double Bar Graphs

A double bar graph displays two sets of data simultaneously side-by-side using pairs of bars. It is ideal for comparing changes over time (such as marks in Term 1 vs Term 2, or sales in 2025 vs 2026).

2. Chance & Probability

Some events are certain to happen ($P = 1$), some are impossible ($P = 0$), and others may or may not happen ($0 < P < 1$).

$$\mathbf{P(\text{Event}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}}$$

Tossing a fair coin: $P(\text{Heads}) = \frac{1}{2}$
Rolling a standard 6-sided die: $P(\text{getting a 5}) = \frac{1}{6}$
$P(\text{getting an even number on a die}) = \frac{3}{6} = \frac{1}{2}$ (favorable: $2, 4, 6$)

3. Concrete Worked Example

Example: A bag contains $4$ red balls and $6$ blue balls. If one ball is drawn at random, what is the probability of drawing a red ball?

Total possible outcomes: $4 + 6 = 10\text{ balls}$

Favorable outcomes (red): $4\text{ balls}$

$$P(\text{Red}) = \frac{4}{10} = \mathbf{\frac{2}{5}} \quad (\text{or } 0.4)$$

4. Pitfall & Examiner Trap

⚠️ Trap: Probability Greater Than 1 or Negative
Probability is ALWAYS between $0$ and $1$ inclusive ($0 \le P \le 1$). If your answer is $1.5$ or negative, check your calculation immediately!

5. Why This Matters in Life

Meteorologists express rain forecasts as probabilities ("80% chance of rain") based on satellite cloud density models.

Visual Learning & Conceptual Map

The Three Central Tendency Pillars

Different lenses to find the typical value of a dataset

MEAN

$\frac{\text{Sum}}{\text{Count}}$

Levels out all values

MEDIAN

Middle Item

After ascending sort

MODE

Most Frequent

Highest tally count

Chapter Summary & 10 Key Takeaways

Takeaway 1

Statistical Question: A question whose answer varies across individuals and requires data collection.

Takeaway 2

Range: The difference between the highest and lowest values in a dataset ($\text{Highest} - \text{Lowest}$).

Takeaway 3

Arithmetic Mean: The sum of observations divided by the number of observations (balance point).

Takeaway 4

Median: The physical middle observation when data is arranged in ascending order.

Takeaway 5

Mode: The observation with the highest frequency of occurrence.

Takeaway 6

Double Bar Graph: Compares two related datasets side-by-side using paired bars and a legend.

Takeaway 7

Probability: Ratio of favorable outcomes to total possible outcomes ($0 \le P \le 1$).

Check Your Understanding (Diagnostic Practice Questions)

Diagnostic questions testing core conceptual clarity. Answers are hidden initially — solve each problem first, then click to reveal the step-by-step verified solution.

Find the mean of the first five natural numbers.

Reveal Answer & Explanation

Answer: $3$
First five natural numbers: $1, 2, 3, 4, 5$. $\text{Sum} = 15$. $\text{Mean} = 15 \div 5 = 3$.

Find the mode and median of the scores: $4, 6, 7, 5, 3, 5, 8, 5, 2$

Reveal Answer & Explanation

Answer: $\text{Mode} = 5$, $\text{Median} = 5$
Sort data: $2, 3, 4, 5, \mathbf{5}, 5, 6, 7, 8$. Middle is $5$. $5$ appears 3 times (mode).

A die is thrown once. What is the probability of getting a prime number?

Reveal Answer & Explanation

Answer: $\frac{1}{2}$
Total outcomes: $\{1, 2, 3, 4, 5, 6\}$ (6 outcomes). Prime outcomes: $\{2, 3, 5\}$ (3 outcomes). $P = \frac{3}{6} = \frac{1}{2}$.

The mean of 5 numbers is 20. If one number is excluded, their mean becomes 18. Find the excluded number.

Reveal Answer & Explanation

Answer: $28$
Original sum $= 5 \times 20 = 100$. New sum of 4 numbers $= 4 \times 18 = 72$. Excluded number $= 100 - 72 = 28$.

Which measure of central tendency is best suited to decide which shirt size a factory should produce the most of?

Reveal Answer & Explanation

Answer: Mode
The mode identifies the most popular item size demanded by consumers.

Finished Studying This Chapter?

READY TO PRACTICE?

Timed CBT Practice Tests (Exam Simulator)

Put your concepts to the test with official curriculum-aligned Foundation and Advanced practice tests. Get instant accuracy scores, time metrics, and step-by-step verified explanations.

Foundation Test

15 MCQs • Core Concepts

Advanced Test

15 MCQs • HOTS & Traps