Connecting the Dots…

How long is a minute?

Two groups of children were asked to estimate the length of 1 minute. They start by closing their eyes and then open them when they think 1 minute has passed. Of course, they are not supposed to count while their eyes are closed. The dot plots below show after how many seconds the children opened their eyes.

Discuss how well both the groups fared at this activity. Describe and compare the variability in data and their central tendency.

Spend sufficient time observing the data presented in this table. Share your findings with the class.

These are some prompts for you to probe —

• Changes in the heights of boys or girls of a certain age from 1989 to 2019.
• The heights of boys vs. girls at different ages in a particular year.
• Changes in height between successive ages in boys and girls in 2019.

Connect the Dots...

A number lock has a 3-digit code. Find the code using the hints below.

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.

Try the activity above on your own. Collect data for 7 or more attempts and find the average.

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?

Two friends are training to run a 100 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?

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.

Find the median of onion prices in Yahapur and Wahapur.

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, —, 10, 25, 2, —, 2, 4. Find the mean and median. How would you describe this data?

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?

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?

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

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?

The weights of some sumo wrestlers and ballet dancers are: Sumo wrestlers: 295.2 kg, 250.7 kg, 234.1 kg, 221.0 kg, 200.9 kg. Ballet dancers: 40.3 kg, 37.6 kg, 38.8 kg, 45.5 kg, 44.1 kg, 48.2 kg. Approximately how many times heavier is a sumo wrestler compared to a ballet dancer?

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?

(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?

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.

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°C. Can you guess which two months these days might belong to?

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’?

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.

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?

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.

Consider this data collected from a survey of a colony.

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

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?

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

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.

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.

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.

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.

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.

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.

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.

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?

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?

The runs scored by Shubman and Yashasvi in a cricket series are given in the table below. Who do you think performed better?

Context: The table shows the runs scored by Shubman and Yashasvi in a series of matches. Vaishnavi says, "Here, Shubman performed better since his total is 110 runs, while Yashasvi's total is 96 runs".

Q. What do you think of Vaishnavi's statement?

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.

Know Your Onions!

The table shows the monthly price of onions, in rupees per kilogram (kg), at two towns. Where are onions costlier, according to you?

Context: The table shows the monthly price of onions, in rupees per kilogram (kg), at two towns, Yahapur and Wahapur.

Q. Can you think of any other ways to compare the data?

Context: The dot plots show the monthly price of onions in Yahapur and Wahapur, as compared to the tables of monthly prices.

Q. Does this visualisation capture all the data presented in the tables earlier?

Context: The dot plots show the monthly price of onions in Yahapur and Wahapur.

Q. Looking at it, can we tell the price of onions in Yahapur in the month of January?

Context: The monthly prices of onions (in ₹) at Yahapur and Wahapur are given in the tables.

Q. Find the average price of onions at Yahapur and Wahapur.

What else do you wonder about?

Context: The heights of the family members of Yaangba and Poovizhi are as follows:

Yaangba's family: 169 cm, 173 cm, 155 cm, 165 cm, 160 cm, 164 cm.

Poovizhi's family: 170 cm, 173 cm, 165 cm, 118 cm, 175 cm.

Q. Find the average height of each family. Can we say that Yaangba's family is taller than Poovizhi's family?

Context: The heights of the family members of Yaangba and Poovizhi are: Yaangba's family: 169 cm, 173 cm, 155 cm, 165 cm, 160 cm, 164 cm. Poovizhi's family: 170 cm, 173 cm, 165 cm, 118 cm, 175 cm.

Q. Can you think of any other number that can represent the data better?

Context: The heights of the family members of Yaangba and Poovizhi are: Yaangba's family: 169 cm, 173 cm, 155 cm, 165 cm, 160 cm, 164 cm. Poovizhi's family: 170 cm, 173 cm, 165 cm, 118 cm, 175 cm.

Q. In this case, does the median represent the heights of the families better than the average?

Context: Poovizhi's family heights are 118 cm, 165 cm, 170 cm, 173 cm, and 175 cm.

Q. Find the mean and median in Poovizhi's data without the outlier value 118. What change do you notice?

Are you a bookworm?

After the summer vacation, a class teacher asked his class how many short stories they had read. Each student answered the number of stories read on a piece of paper, as shown below. Find the mean and median number of short stories read. Before calculating them, can you guess whether the mean will be less than or greater than the median?

Mark the data, the mean, and the median on the dot plot below.

Context: A class teacher asked his class how many short stories they had read. The number of stories read by each student are: 6, 8, 5, 15, 3, 0, 2, 7, 12, 40, 10, 0, 8, 5, 1.

Q. Which of the values would you consider an outlier?

Context: A class teacher asked his class how many short stories they had read. The number of stories read by each student are: 6, 8, 5, 15, 3, 0, 2, 7, 12, 40, 10, 0, 8, 5, 1.

Q. Find the mean and median in the absence of the outlier. What change do you notice?

Are We on the Same Page?

Do you read newspapers? Have you noticed how many pages a newspaper has on different days of the week — is it the same or different?

The list below shows the number of pages for a particular newspaper from Monday to Sunday: 16, 18, 20, 22, 26, 16, 10.

Mark the data, the mean, and the median on the dot plot below.

In the three examples we considered — the heights, short-stories, and newspaper pages — observe the variability in data when:

(a) the mean and median are close to each other (b) the mean and median are comparatively far apart, with mean < median (c) the mean and median are comparatively far apart, with mean > median

Discuss the effect on the mean and median when outliers are present on both sides. You may take some example data to examine and explain this.

Context: The heights of boys and girls in a Grade 5 class are shown in the dot plots on the previous page, with a whole class mean of 144.4 cm.

Q. How many students are taller than the class' average height?

Context: The heights of boys and girls in a Grade 5 class are shown in the dot plots on the previous page, with a whole class mean of 144.4 cm.

Q. How many boys are taller than the class' average height?

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

Context: Refer to the double column graph showing monthly onion prices in Yahapur and Wahapur.

Q. What is the scale used in this graph?

Context: Refer to the double column graph showing monthly onion prices in Yahapur and Wahapur.

Q. Is it now easier to compare month-wise prices in both places?

Context: Look at the graph showing the number of worldwide rocket launches by different organisations.

Q. Share your observations (you may take the teacher's help to identify the countries these organisations belong to).

Context: Look at the graph showing the number of worldwide rocket launches by different organisations.

Q. Notice how the graph is organised, what scale is used, and what patterns the data shows.

Identify which of the following statements can be justified using this data.

(a) All organisations launched more rockets than the previous years.

(b) Only an organisation from the USA launched more than 50 rockets in a single year.

(c) The total number of rockets launched by France in all 3 years is less than 40.

(d) The average number of rockets launched by CASC in these 3 years is around 40.

(e) ISRO launched more rockets than Galactic Energy in these 3 years.

(f) Russia launched more than 60 rockets in these 3 years.

List the organisations that have consistently launched more rockets every year.

Estimate the total number of rockets launched worldwide in 2023.

(a) less than 200

(b) 200 to 400

(c) 400 to 600

(d) more than 600

Summer and Winter at the Same Time

The tables below show data related to weather in two cities in different countries. The numbers given are in hours. Can you guess what the data might be related to?

Context: City 1 and City 2 are two cities in different countries. The average daily sunshine hours/daylight hours for these cities are shown in the graph.

Q. Does this give some idea of where these two cities are located?

Answer the following questions based on the graph:

1. Can we tell who batted first? Who won the match?

2. How many runs did the blue team score in over 12?

3. In which over did the red team score the least number of runs?

4. Is it easy to tell the target set by the team batting first?

Following are the dot plots of heights of boys (in blue) and girls (in orange) of Grades 6, 7 and 8 (in that order) of two different schools. What do you notice? Share your observations.

Which of the following statements can be justified using the data?

1. The average heights of both boys and girls at every age increased from 1989 to 2019.
2. The average height of 13-year-old girls in 1989 is more than the average height of 14-year-old girls in 2009.
3. The average height of 15-year-old boys in 2019 is more than the average height of 16-year-old boys in 1989.
4. All girls aged 13 are taller than all girls aged 11.
5. Throughout the age period 5 to 19, the average boy's height is more than the average girl's height.
6. Boys keep growing even beyond age 19.

In 2019, between which two successive ages from 5 to 19 did boys grow the most? Between which two successive ages from 5 to 19 did girls grow most?

Suppose the average height of a newborn is 50 cm. Estimate the average height of young children of ages 1 to 4.

Based on the trend observed in the table, write your estimates of the heights of boys and girls for ages 5 to 19 in the year 2029.

How is the graph organised? What information is presented?

What do you find interesting?