Class 7 Maths Chapter 5 Connecting the Dots notes and book solutions from Ganita Prakash Part 2 with easy explanations, important concepts, examples and complete textbook question answers for revision and exam preparation.
Class 7 Mathematics – Chapter 5
Connecting the Dots…
Ganita Prakash | Grade 7 | Part-II
Easy Notes, Concepts and Complete Book Solutions
Chapter at a Glance
Main idea:This chapter teaches us how to ask statistical questions,
collect and compare data, find representative values such as
mean and median, identify outliers, and understand data through
dot plots and clustered/double bar graphs.
Key words:Data, statistical question, statistical statement, mean,
arithmetic mean, median, outlier, variability, central tendency,
dot plot, clustered column graph, double bar graph and scale.
Mean = Sum of all values ÷ Number of values
Median = Middle value after arranging the data in order.
If there are an even number of values:Median = Average of the two middle values.
If there are an even number of values:Median = Average of the two middle values.
Remember:A zero is a real data value.A dash showing that a player did not play is not a zero and
should not be counted as a played match.
5.1 Of Questions and Statements
Statistical statement:A claim or summary about a phenomenon expressed using numbers,
proportions, probabilities or predictions.
Statistical question:A question that can be answered by collecting and analysing data.Such a question normally expects variation in the answers.
Your teacher tells you that they are meeting two of their
childhood friends this evening. One is 5 feet tall and the
other is 6 feet tall. What is your guess as to each friend’s
gender based on this information?
Page 97
Which of the following are statistical questions?
(a) What is the price of a tennis ball in India?
(b) How old are the dogs that live on this street?
(c) What fraction of the students in your class like walking up a hill?
(d) Do you like reading?
(e) Approximately how many bricks are in this wall?
(f) Who was the best bowler in the match yesterday?
(g) What was the rainfall pattern in Barmer last year? Page 98
(a) What is the price of a tennis ball in India?
(b) How old are the dogs that live on this street?
(c) What fraction of the students in your class like walking up a hill?
(d) Do you like reading?
(e) Approximately how many bricks are in this wall?
(f) Who was the best bowler in the match yesterday?
(g) What was the rainfall pattern in Barmer last year? Page 98
5.2 Representative Values
A representative value is one number that helps us describe
a group of numbers.The chapter introduces the arithmetic mean and median.
The runs scored by Shubman and Yashasvi in a cricket series
are given in the table below. Who do you think performed better?
Page 98
| Match 1 | Match 2 | Match 3 | Match 4 | |
|---|---|---|---|---|
| Shubman | 0 | 17 | 21 | 90 |
| Yashasvi | 67 | 55 | 18 | 35 |
The table below shows the runs scored by these two players
in another series. Who do you think performed better in this
series?
Page 99
| Match 1 | Match 2 | Match 3 | Match 4 | Match 5 | |
|---|---|---|---|---|---|
| Shubman | 23 | 07 | 10 | 52 | 18 |
| Yashasvi | 26 | 53 | 02 | — | 15 |
What do you think of Vaishnavi’s statement?
Page 99
Can a single number act as a representative of a group of
numbers? For example, can we represent Shubman’s or Yashasvi’s
batting in this series with one number? Discuss.
Page 99
Find the arithmetic mean of the following numbers:6, 8, 10, 12, 14
Page 100
Mean and Median – Easy Explanation
Mean:Add all the numbers and divide the total by the number
of values.
Mean = Total of observations ÷ Number of observations
Median:First arrange the numbers from smallest to largest.Then find the middle number.
If the number of observations is even, there are two middle
numbers.Add these two numbers and divide by 2.
The number of short stories read by a student over 16 weeks
is:
6, 8, 15, 5, 0, 3, 0, 2, 7, 12, 40, 10, 5, 0, 1, 8 Page 107
6, 8, 15, 5, 0, 3, 0, 2, 7, 12, 40, 10, 5, 0, 1, 8 Page 107
Why can an outlier affect the mean more than the median?
Page 107
Working with Data – Wahapur Onion Prices
The price of onions per kilogram in Wahapur over 12 months
was:
19, 17, 23, 30, 38, 35, 42, 39, 53, 60, 52, 42 Data Activity
19, 17, 23, 30, 38, 35, 42, 39, 53, 60, 52, 42 Data Activity
Reading a Double Bar Graph – Rocket Launches
A double bar graph uses two bars for each category.It helps us compare two sets of data.Always check:
- Title of the graph
- Names of the two data sets
- Scale on the vertical axis
- Categories on the horizontal axis
Look at the rocket launch graph and answer the questions
based on the data shown.
Page 117
Which of the following statements are justified by the
rocket-launch graph?
(a) Every organisation increased its launches every year.
(b) Only an organisation from the USA launched more than 50 rockets in a single year.
(c) Arianespace launched fewer than 40 rockets in total over the three years.
(d) The average number of launches by CASC was around 40.
(e) Every organisation launched more rockets in 2023 than in 2021.
(f) SpaceX had the highest number of launches in every year. Page 117
(a) Every organisation increased its launches every year.
(b) Only an organisation from the USA launched more than 50 rockets in a single year.
(c) Arianespace launched fewer than 40 rockets in total over the three years.
(d) The average number of launches by CASC was around 40.
(e) Every organisation launched more rockets in 2023 than in 2021.
(f) SpaceX had the highest number of launches in every year. Page 117
Reading a Cricket Double Bar Graph
Study the cricket double bar graph and answer the questions.
Page 122
Dot Plots
A dot plot shows how often each value occurs.Each dot represents one observation.If several dots are stacked above the same number, that number
occurs several times.
Study the dot plots of the number of pockets in the clothes
and answer the statements given in the textbook.
Page 129
The table gives the runs scored by three players.Who has the highest average?
Page 129
Working with Height Data
The heights of students in a class are given in the textbook.
Find the mean, identify the median and answer the questions
based on the data.
Page 130
There are two 7th grade sections at a school. Each section
has 15 boys and 15 girls. In one section, the mean height of
students is 154.2 cm. From this information, what must be true
about the mean height of students in the other section?
(a) The mean height of students in the other section is 154.2 cm.
(b) The mean height of students in the other section is less than 154.2 cm.
(c) The mean height of students in the other section is more than 154.2 cm.
(d) The mean height of students in the other section cannot be determined. Page 130
(a) The mean height of students in the other section is 154.2 cm.
(b) The mean height of students in the other section is less than 154.2 cm.
(c) The mean height of students in the other section is more than 154.2 cm.
(d) The mean height of students in the other section cannot be determined. Page 130
Standing Tall in the Storm – Skyscraper Data
Write estimated values for the number of skyscrapers in
New York, Tokyo and London.Are the following statements valid?
(i) Only 12 cities have more skyscrapers than Mumbai.
(ii) Only 7 cities have fewer skyscrapers than Mumbai.
(iii) The tallest building in the world is in Hong Kong. Page 131
(i) Only 12 cities have more skyscrapers than Mumbai.
(ii) Only 7 cities have fewer skyscrapers than Mumbai.
(iii) The tallest building in the world is in Hong Kong. Page 131
Estimate and then measure the objects listed in the following
table. Draw a double bar graph based on the data.How accurate were your estimates?Find the average difference between the estimated and measured
values.
Page 131
Sudoku Time Data
Aditi likes solving puzzles. She recently started attempting
the ‘Easy’ level Sudoku puzzles.The time she took in seconds to solve these puzzles are:
410, 400, 370, 340, 360, 400, 320, 330, 310, 320, 290, 380, 280, 270, 230, 220, 240
The first nine values correspond to Week 1 and the rest to Week 2.
(a) Construct a dot plot below showing the data for both weeks.
(b) Describe the mean, median, and any observations you may have about the data. Page 132
410, 400, 370, 340, 360, 400, 320, 330, 310, 320, 290, 380, 280, 270, 230, 220, 240
The first nine values correspond to Week 1 and the rest to Week 2.
(a) Construct a dot plot below showing the data for both weeks.
(b) Describe the mean, median, and any observations you may have about the data. Page 132
Individual Project – How Long is a Sentence?
Pick any two textbooks from different subjects.Choose any page with a lot of text from each book.
(i) Use a dot plot to describe how many words the sentences have on each page.
(ii) Compare the data of both the pages using mean and median. Page 132
(i) Use a dot plot to describe how many words the sentences have on each page.
(ii) Compare the data of both the pages using mean and median. Page 132
Individual Project – What is in a Name?
Write down the names of all of your classmates.Find the mean and median name length.Visualise the data and describe its variability and central
tendency.
Page 132
(iii) Which starting letters are more popular?
Which are less popular?
(iv) What is the median starting letter?What does this say about the number of names starting with the letters A–M and N–Z?
(v) Plot a double-bar graph showing the number of boys’ names and girls’ names that:
• start and end with vowels,
• start with vowels and end with consonants,
• start with consonants and end with vowels,
• start and end with consonants. Page 133
(iv) What is the median starting letter?What does this say about the number of names starting with the letters A–M and N–Z?
(v) Plot a double-bar graph showing the number of boys’ names and girls’ names that:
• start and end with vowels,
• start with vowels and end with consonants,
• start with consonants and end with vowels,
• start and end with consonants. Page 133
Long-Term Project – In and Out
Track how many times you step out of your house in a day.Do this for a month.
(i) Describe the variability and central tendency of this data. Make a dot plot.
(ii) Do you find anything interesting about this data? Share your observations.
(iii) You can ask any of your family members or friends to do this as well. Page 133
(i) Describe the variability and central tendency of this data. Make a dot plot.
(ii) Do you find anything interesting about this data? Share your observations.
(iii) You can ask any of your family members or friends to do this as well. Page 133
Small-Group Project
Pick at least one of the following.Make groups of 8 to 10.Collect data individually as needed.Put together everyone’s data and do the appropriate analysis
and visualisation.
(a) Our heights vs. our family’s heights
Collect the heights of your family members.
(i) Make a dot plot showing heights of just your family members. Describe its variability and central tendency.
(ii) Make a double-bar graph showing each student’s height next to their family’s mean height.
(iii) Look at everyone’s data and share your observations.
(b) Estimating time
Check the time and close your eyes.Open them when you think 1 minute has passed.Do not count.Note down after how many seconds you opened your eyes.Collect this data for yourself and for your family members.Repeat this activity to estimate 3 minutes.
(i) Make two dot plots, for 1 minute and 3 minutes, showing estimates of just your family members.
(ii) Mark these on the respective dot plots.Describe their variability and central tendency.
(iii) Make a double-bar graph showing each family’s mean 1-minute estimate and mean 3-minute estimate.
(iv) Look at everyone’s data and share your observations. Pages 133–134
(a) Our heights vs. our family’s heights
Collect the heights of your family members.
(i) Make a dot plot showing heights of just your family members. Describe its variability and central tendency.
(ii) Make a double-bar graph showing each student’s height next to their family’s mean height.
(iii) Look at everyone’s data and share your observations.
(b) Estimating time
Check the time and close your eyes.Open them when you think 1 minute has passed.Do not count.Note down after how many seconds you opened your eyes.Collect this data for yourself and for your family members.Repeat this activity to estimate 3 minutes.
(i) Make two dot plots, for 1 minute and 3 minutes, showing estimates of just your family members.
(ii) Mark these on the respective dot plots.Describe their variability and central tendency.
(iii) Make a double-bar graph showing each family’s mean 1-minute estimate and mean 3-minute estimate.
(iv) Look at everyone’s data and share your observations. Pages 133–134
Quick Revision
1. Statistical question:A question answered by collecting data.
2. Mean:Add all values and divide by the number of values.
3. Median:Arrange the data and take the middle value.For an even number of values, average the two middle values.
4. Outlier:A value that is very different from the rest of the data.
5. Dot plot:A graph that shows how frequently values occur.It helps us see clustering and spread.
6. Double bar graph:Places two bars side by side for each category so that
two data sets can be compared.
Always check:
What is the scale?
What are the minimum and maximum values?
What is the mean?
What is the median?
Is there an outlier?
What is the scale?
What are the minimum and maximum values?
What is the mean?
What is the median?
Is there an outlier?
Prepare for your exams with this easy and student-friendly worksheet based on Class 7 Maths Chapter 5 from Ganita Prakash Part 2. Practice all the questions carefully to revise the chapter, strengthen your concepts, and improve your mathematical understanding.
CLASS 7 • MATHEMATICS PART 2
Class 7 Maths Part 2 Chapter 5 Worksheet
Practice worksheet for Class 7 Mathematics Part 2 Chapter 5 with important questions, extra practice and answer key.
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