Connecting the Dots — Class 7 Mathematics NCERT Solutions (Free)

Free step-by-step NCERT solutions for Class 7 Mathematics chapter "Connecting the Dots" — 7 important questions with detailed answers for CBSE board exam preparation.

TL;DR: Free step-by-step NCERT solutions for Class 7 Mathematics chapter "Connecting the Dots" — 7 important questions with detailed answers for CBSE board e…

By Syllab.in · Updated Jun 14, 2026

Key Questions Covered:

Define mean, median, and mode. Find all three for the data set: 3, 7, 5, 3, 9…
A student scores: 80, 85, 78, 92, 88 in five tests. Calculate the mean and fi…
Interpret a bar graph showing monthly rainfall: Jan-2, Feb-3, Mar-5, Apr-8, M…
Define probability. A die is rolled. What is the probability of getting an ev…
A bag contains 5 red balls, 3 blue balls, and 2 green balls. If one ball is d…
Find the median and mode of the following marks: 45, 50, 55, 50, 60, 45, 55, …
+ 1 more questions in the full chapter

Solutions Summary:

Question	Status
Define mean, median, and mode. Find all three for the dat…	✓ Solved
A student scores: 80, 85, 78, 92, 88 in five tests. Calcu…	✓ Solved
Interpret a bar graph showing monthly rainfall: Jan-2, Fe…	✓ Solved
Define probability. A die is rolled. What is the probabil…	✓ Solved
A bag contains 5 red balls, 3 blue balls, and 2 green bal…	✓ Solved
Find the median and mode of the following marks: 45, 50, …	✓ Solved

Showing 6 of 7 questions

Q1: Define mean, median, and mode. Find all three for the data set: 3, 7, 5, 3, 9, 3, 5.

Definitions: 1. Mean (Average): The mean is the sum of all values divided by the number of values. Formula: Mean = (Sum of all values) / (Number of values) 2. Median: The median is the middle value when data is arranged in order. If the number of values is even, median is the average of two middle values. 3. Mode: The mode is the value that appears most frequently (most often) in the data set. A data set can have no mode, one mode, or multiple modes. --- For the data set: 3, 7, 5, 3, 9, 3, ...

Q2: A student scores: 80, 85, 78, 92, 88 in five tests. Calculate the mean and find how much above or below the mean each score is.

Given scores: 80, 85, 78, 92, 88 Step 1: Calculate the mean Sum = 80 + 85 + 78 + 92 + 88 = 423 Number of scores = 5 Mean = 423 ÷ 5 = 84.6 Step 2: Find deviation from mean for each score Deviation = Score - Mean Score 1: 80 - 84.6 = -4.6 (below mean by 4.6) Score 2: 85 - 84.6 = +0.4 (above mean by 0.4) Score 3: 78 - 84.6 = -6.6 (below mean by 6.6) Score 4: 92 - 84.6 = +7.4 (above mean by 7.4) Score 5: 88 - 84.6 = +3.4 (above mean by 3.4) Step 3: Summary table | Score | Deviation from Mean | ...

Q3: Interpret a bar graph showing monthly rainfall: Jan-2, Feb-3, Mar-5, Apr-8, May-10, Jun-12 cm. Find the total and average rainfall.

Monthly Rainfall Data (in cm): January: 2 cm February: 3 cm March: 5 cm April: 8 cm May: 10 cm June: 12 cm --- Bar Graph Description: The bar graph would show: • X-axis: Months (Jan, Feb, Mar, Apr, May, Jun) • Y-axis: Rainfall in cm (scale: 0 to 12 cm) • Bar heights increasing from Jan (2) to Jun (12) Visual pattern: June has the highest rainfall (12 cm) January has the lowest rainfall (2 cm) Rainfall increases continuously from January to June --- Calculating Total Rainfall: Total = 2 + 3...

Q4: Define probability. A die is rolled. What is the probability of getting an even number?

Probability: Probability is the chance or likelihood of an event occurring. It is expressed as a ratio between 0 and 1, where: 0 = impossible event (will not happen) 1 = certain event (will definitely happen) Formula: Probability = (Number of favorable outcomes) / (Total number of possible outcomes) --- Problem: A die is rolled. What is the probability of getting an even number? Step 1: Identify all possible outcomes When a die is rolled, the possible outcomes are: 1, 2, 3, 4, 5, 6 Total num...

Q5: A bag contains 5 red balls, 3 blue balls, and 2 green balls. If one ball is drawn at random, find the probability of drawing a red ball and a non-red ball.

Given: Red balls: 5 Blue balls: 3 Green balls: 2 Step 1: Find total number of balls Total = 5 + 3 + 2 = 10 balls --- Part 1: Probability of drawing a red ball Step 2a: Identify favorable outcomes Favorable outcomes (red balls) = 5 Step 3a: Calculate probability P(red) = (Number of red balls) / (Total balls) P(red) = 5/10 = 1/2 = 0.5 P(red) = 50% --- Part 2: Probability of drawing a non-red ball Step 2b: Identify favorable outcomes Non-red balls = Blue balls + Green balls Non-red balls = ...

Q6: Find the median and mode of the following marks: 45, 50, 55, 50, 60, 45, 55, 50, 65.

Given marks: 45, 50, 55, 50, 60, 45, 55, 50, 65 Step 1: Arrange marks in ascending order 45, 45, 50, 50, 50, 55, 55, 60, 65 Number of values = 9 (odd number) --- Finding the Median: Step 2: Find the middle position For odd number of values: Median position = (n + 1)/2 Median position = (9 + 1)/2 = 10/2 = 5th position Step 3: Identify the median Counting from the ordered list: 1st: 45, 2nd: 45, 3rd: 50, 4th: 50, 5th: 50, ... Median = 50 --- Finding the Mode: Step 4: Count frequency of ea...

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