Chapter 5 Connecting the Dots... (Class 7 - Latest Maths NCERT (Ganita Prakash II) Solutions)

Question 1. Shreyas is playing with a bat and a ball — but not cricket. He counts the number of times he can bounce the ball on the bat before it falls to the ground. The data for $8$ attempts is $6, 2, 9, 5, 4, 6, 3, 5$. Calculate the average number of bounces of the ball that Shreyas is able to make with his bat.

Question 2. Try the activity above on your own.

Collect data for $7$ or more attempts and find the average.

Question 3. Identify a flowering plant in your neighbourhood. Track the number of flowers that bloom every day over a week during its flowering season. What is the average number of flowers that bloomed per day?

Question 4. Two friends are training to run a $100\text{ m}$ race. Their running times over the past week are given in seconds — Nikhil: $17, 18, 17, 16, 19, 17, 18$; Sunil: $20, 18, 18, 17, 16, 16, 17$. Who on average ran quicker?

Question 5. The enrolment in a school during six consecutive years was as follows: $1555, 1670, 1750, 2013, 2040, 2126$. Find the mean enrolment in the school during this period.

Question 1. Find the median of onion prices in Yahapur and Wahapur.

Question 2. Sanskruti asked her class how many domestic animals and pets each had at home. Some of the students were absent.

The data values are: $0, 1, 0, 4, 8, 0, 0, 2, 1, 1, 5, 3, 4, 0, 0, \text{—}, 10, 25, 2, \text{—}, 2, 4$.

Find the mean and median. How would you describe this data?

Question 3. Rintu takes care of a date-palm tree farm in Habra. The heights of the trees (in feet) in his farm are given as: $50, 45, 43, 52, 61, 63, 46, 55, 60, 55, 59, 56, 56, 49, 54, 65, 66, 51, 44, 58, 60, 54, 52, 57, 61, 62, 60, 60, 67$.

Fill the dot plot, and mark the mean and median. How would you describe the heights of these palm trees? Can you think of quicker ways to find the mean? How many trees are shorter than the average height?

Question 4. The daily water usage from a tap was measured. The usage in liters for the first few days are: $5.6, 8, 3.09, 12.9, 6.5, 12.1, 11.3, 20.5, 7.4$.

(a) Can the mean or median daily usage lie between $25$ and $30$? Justify your claim using the meaning of mean and median.

(b) Can the mean or median be lesser than the minimum value or greater than the maximum value in a data?

Question 5. The weights of a few newborn babies are given in kgs. Fill the dot plot provided below. Analyse and compare this data.

Question 6. The dot plots of heights of another section of Grade 5 students of the same school are shown below. Can you share your observations? What can we infer from the dot plots and the central tendency measures?

Whole class: Mean $= 141.21$, Median $= 142.5$

Boys: Mean $= 142.05$, Median $= 143$

Girls: Mean $= 140.14$, Median $= 140$

Compare the heights of the two sections. Share your observations.

Question 7. The weights of some sumo wrestlers and ballet dancers are:

Sumo wrestlers: $295.2\text{ kg}, 250.7\text{ kg}, 234.1\text{ kg}, 221.0\text{ kg}, 200.9\text{ kg}$.

Ballet dancers: $40.3\text{ kg}, 37.6\text{ kg}, 38.8\text{ kg}, 45.5\text{ kg}, 44.1\text{ kg}, 48.2\text{ kg}$.

Approximately how many times heavier is a sumo wrestler compared to a ballet dancer?

Question 1. The following infographic shows the speeds of a few animals in air, on land, and in water. Can we call this graph a bar graph?

The peregrine falcon is the world's fastest animal. It hunts by diving at high speed and striking a pigeon or other bird in midair.

The Australian tiger beetle moves at a blistering pace—about $120$ body lengths per second. Its eyes can't process images fast enough to keep up, so at top speed this beetle is running blind.

(a) What is the scale used in this graph?

(b) What did you find interesting in this infographic? What do you want to explore further?

(c) Identify a pair of creatures where one’s speed is about twice that of the other.

(d) Can we say that a sailfish is about $4$ times faster than a humpback whale? Can we say that a sailfish is the fastest aquatic animal in the world?

Question 2. Preyashi asked her students ‘If you were to get a super power to become aquatic (water-borne), aerial (air-borne), or spaceborne which one would you choose?’. The responses are shown below. Some chose none. Draw a double-bar graph comparing how both grades chose each option. Choose an appropriate scale.

Question 3. The temperature variation over two days in different months in Jodhpur, Rajasthan, is given below. Draw a double-bar graph. Use the scale $1$ unit $= 4^\circ\text{C}$. Can you guess which two months these days might belong to?

Question 4. The following clustered-bar graph shows the number of electric vehicles registered in some states every year from $2022$ to $2024$.

(a) The data (rounded-off to thousands) for the states of Gujarat and Delhi are given in the table below. Mark the corresponding bars on the bar graph. (It is enough if you place the top of the bars between the two appropriate vertical guidelines.)

(b) Notice how the graph is organised, what scale is used, and what patterns the data shows.

(c) How would you describe the change for various states between $2022$ and $2024$?

(d) Approximately how many more registrations did Assam get in $2023$ compared to $2022$?

(e) How many times more did the registrations in West Bengal increase from $2022$ to $2024$?

(f) Is this statement correct — ‘There were very few new registrations in Uttarakhand in $2023$ and $2024$, as the increase in the bar lengths is minimal’?

Question 1. The dot plots below show the distribution of the number of pockets on clothing for a group of boys and for a group of girls.

Based on the dot plots, which of the following statements are true?

(a) The data varies more for the boys than for the girls.

(b) The median number of pockets for the boys is more than that for the girls.

(c) The mean number of pockets for the girls is more than that for the boys.

(d) The maximum number of pockets for boys is greater than that for the girls.

Question 2. The following table shows the points scored by each player in four games:

Now answer the following questions:

(a) Find the average number of points scored per game by A.

(b) To find the mean number of points scored per game by C, would you divide the total points by $3$ or by $4$? Why? What about B?

(c) Who is the best performer?

Question 3. The marks (out of $100$) obtained by a group of students in a General Knowledge quiz are $85, 76, 90, 85, 39, 48, 56, 95, 81$ and $75$. Another group’s scores in the same quiz are $68, 59, 73, 86, 47, 79, 90, 93$ and $86$. Compare and describe both the groups performance using, mean and median.

Question 4. Consider this data collected from a survey of a colony.

Choose an appropriate scale and draw a double-bar graph. Write down your observations.

Question 5. Consider a group of $17$ students with the following heights (in cm): $106, 110, 123, 125, 117, 120, 112, 115, 110, 120, 115, 102, 115, 115, 109, 115, 101$. The sports teacher wants to divide the class into two groups so that each group has an equal number of students: one group has students with height less than a particular height and the other group has students with heights greater than the particular height. Suggest a way to do this. Can you guess the age of these students based on the tabular data in the ‘Telling Tall Tales’ section?

Question 6. Describe the mean and median of heights of your class. You can visualise the heights on a dot plot.

Question 7. 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 $154.2\text{ cm}$. 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 $154.2\text{ cm}$.

(b) The mean height of students in the other section is less than $154.2\text{ cm}$.

(c) The mean height of students in the other section is more than $154.2\text{ cm}$.

(d) The mean height of students in the other section cannot be determined.

Question 8. Standing tall in the storm.

(a) Write estimated values for the number of skyscrapers in New York, Tokyo, and London.

(b) 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.

Question 9. 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.

Question 10. 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.

Question 11. Individual Project: Pick at least one of the following:

(a) 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.

(b) What is in a Name? Write down the names of all of your classmates. The following are some interesting things you can do with this data!

(i) Find the mean and median name length (number of letters in a name).

(ii) Visualise the data and describe its variability and central tendency.

(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.

Question 12. Individual project (long term): This requires collecting data over 2 weeks or more.

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.

Question 13. 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 (no counting). 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 its 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.