Connecting the Dots… | FIO

Question 11

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?

Solution

We will carefully look at the dot plots and numbers. We will compare heights of boys and girls.

Step 1 — Understanding the spread of heights

Let us look at the range of heights for each group. The range tells us how spread out the data is.

For girls, the shortest height shown is 126. The tallest height shown is 158. So, girls' heights are between 126 and 158.

For boys, the shortest height shown is 130. The tallest height shown is 148. So, boys' heights are between 130 and 148.

We can see that girls' heights cover a wider range. They are more spread out.

Diagram 1

Step 2 — Identifying the shortest and tallest students

Let us find the shortest and tallest students. We check all three plots.

The shortest height in the whole class is 126. This student is a girl. The tallest height in the whole class is 158. This student is also a girl.

So, both the shortest and tallest students are girls.

Step 3 — Comparing average heights

Let us compare the average heights using the mean and median.

The mean height for girls is 140.14. The mean height for boys is 142.05. The mean height for the whole class is 141.21.

The median height for girls is 140. The median height for boys is 143. The median height for the whole class is 142.5.

We see that the boys' average height is greater than the girls' average height. Boys' mean 142.05 is greater than girls' mean 140.14. Boys' median 143 is greater than girls' median 140. Also, the girls' average height is less than the whole class average.

This means boys are generally taller than girls in this class.

Step 4 — Analyzing mean and median relationship

Let us look at how mean and median compare for each group. This tells us about the shape of the data.

For boys, the mean is 142.05. The median is 143. Here, the mean is less than the median ( $142.05 < 143$ ). This suggests some lower values might be pulling the mean down.

For girls, the mean is 140.14. The median is 140. Here, the mean is greater than the median ( $140.14 > 140$ ). This suggests some higher values might be pulling the mean up.

Step 5 — Comparing with other data

We are asked to compare this data with a previous example. Based on this comparison, we find that the boys and girls of this section are shorter in height.

Answer

(i) The girls' heights are more spread out. They range between 126 and 158. (ii) The boys' heights lie between 130 and 148. (iii) Both the tallest and shortest students in the class are girls. (iv) The girls' average height is less than the whole class average. It is also less than the boys' average height. (v) We can say that boys are generally taller than girls in this class. (vi) For boys' heights, the mean ( $142.05$ ) is less than the median ( $143$ ). This shows a small influence of lower values. (vii) For girls' heights, the mean ( $140.14$ ) is greater than the median ( $140$ ). This shows a small influence of higher values. (viii) On comparing this data with a previous example, we find that the boys and girls of this section are shorter in height.

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Q10

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

Q11

Q12

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?

Q13

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?

(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?

Q14

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.

Q15

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?

Q16

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’?

Q17

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.

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

Q18

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?

Q19

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.

Q20

Consider this data collected from a survey of a colony.

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

Q21

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?

Q22

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

Q23

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.

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

Q24

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.

Q25

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.

Q26

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.

Q27

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.

Q28

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.

Q29

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.