Connecting the Dots... - Chapter 5 Class 7 (Ganita Prakash II)

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.Now,
Average number of bounces Shreyas makes per attempt
= (𝑇𝑜𝑡𝑎𝑙 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑏𝑜𝑢𝑛𝑐𝑒𝑠 𝑆ℎ𝑟𝑒𝑦𝑎𝑠 𝑚𝑎𝑘𝑒𝑠)/(𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑎𝑡𝑡𝑒𝑚𝑝𝑡𝑠)
= (𝟔 + 𝟐 + 𝟗 + 𝟓 + 𝟒 + 𝟔 + 𝟑 + 𝟓)/𝟖
= 40/8
= 5

Try the activity above on your own. Collect data for 7 or more attempts and find the average.Let's say you bounced the ball the following times in 7 attempts:
4, 5, 7, 3, 8, 4, 11

Identify a flowering plant in your neighborhood. 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? Let’s assume this data for every day of the week
Mon: 2, Tue: 3, Wed: 0, Thu: 4, Fri: 2, Sat: 5, Sun: 5

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?We need to find who ran quicker,
i.e. we need to find who took lesser time to run the race

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.Now,
Mean enrolment in the school
= (𝑇𝑜𝑡𝑎𝑙 𝑒𝑛𝑟𝑜𝑙𝑚𝑒𝑛𝑡 𝑖𝑛 𝑡ℎ𝑒 𝑠𝑐ℎ𝑜𝑜𝑙)/(𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑦𝑒𝑎𝑟𝑠)
= (𝟏𝟓𝟓𝟓 + 𝟏𝟔𝟕𝟎 + 𝟏𝟕𝟓𝟎 + 𝟐𝟎𝟏𝟑 + 𝟐𝟎𝟒𝟎 + 𝟐𝟏𝟐𝟔)/𝟔
= (11,154 )/6
Dividing both numerator & denominator by 2
= 5577/3
Dividing both numerator & denominator by 2
= 1,859

Find the median of onion prices in Yahapur and Wahapur.The data is
Month Yahapur
January 25
February 24
March 26
April 28
May 30
June 35
July 39
August 43
September 49
October 56
November 59
December 44
Month Wahapur
January 19
February 17
March 23
April 30
May 38
June 35
July 42
August 39
September 53
October 60
November 52
December 42For Yahapur
Writing data in ascending order
24, 25, 26, 28, 30, 35, 39, 43, 44, 49, 56, 59

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?The dashes (—) represent absent students, so we do not count them. We only calculate using the actual numbers provided.
Thus,
Number of students = 21

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?Let’s first find Median & Mean
Here,
Number of trees = 30

(a) 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.Putting Data in Ascending order
3.09, 5.6, 6.5, 7, 8, 11.3, 12.1, 12.9, 20.5

The weights of a few newborn babies are given in kgs. Fill the dot plot provided below. Analyse and compare this data.Let’s find the Mean and Median for both data – and plot it

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?Comparing the Center (Mean & Median)
Boys:
Mean: 142.05 cm
Median: 143 cm
Girls:
Mean: 140.14 cm
Median: 140 cm

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?We have to compare two groups that are extremely different (like Sumos and Dancers),
To compare, we find a "Representative Value"— that could be Mean or Median
We usually choose Mean unless there is an outlier
In both data, there is no outlier (either very high weight or very low weight – in that data)
This means there is no very light sumo lesser
or very heavy ballerina

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?(a) What is the scale used in this graph?
Notice our Number axis – it goes 0, 16, 32, 48, ….
The difference between each mark is
𝟏𝟔−𝟎=𝟏𝟔
Thus,
the scale is 𝟏 unit =𝟏𝟔" " 𝒌𝒎/𝒉 (kilometres per hour).
(b) What did you find interesting in this infographic? What do you want to explore further?
This is for you to decide!
For me, the most interesting was
"It is interesting that a bird (Peregrine Falcon) is faster than the fastest car on a highway,
or that a tiny insect like the Dragonfly is faster than a huge Humpback Whale."
(c) Identify a pair of creatures where one’s speed is about twice that of the other.
Let's estimate the numbers from the bars:
Sailfish: ∼109" " km/h
Flying Fish: ∼56" " km/h

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.First, we need to count the votes first
For both grades, we count how many 'w' (water), 'a' (air), 's' (space), and 'n' (none).

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?While drawing a bar graph, we follow these steps
First we decide what to put in x-axis and y-axis
We always use numbers in y-axis, so temperature is in y-aixs
And, Time are in y-axis
Then, we find out our Scale
This is given, 1 unit length = 4°C
Lastly, we decide our legend – color to denote which Grade
We choose blue for Day 1, Red for Day 2

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.)
Let’s complete our graph
(b) Notice how the graph is organised, what scale is used, and what patterns the data showsOrganisation:
It is a Clustered Bar Graph.
It groups the data by State (on the x -axis) and uses different colors for years.

(a) 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.Here
The boys' data is clumped between 3 and 6 .
The girls' data is spread out all the way from 0 to 6 . The girls' data varies more.

(a) 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. Now,
Average points scored by A = (𝑻𝒐𝒕𝒂𝒍 𝒑𝒐𝒊𝒏𝒕𝒔 𝒔𝒄𝒐𝒓𝒆𝒅 𝒃𝒚 𝑨)/(𝑵𝒖𝒎𝒃𝒆𝒓 𝒐𝒇 𝒈𝒂𝒎𝒆𝒔 𝒑𝒍𝒂𝒚𝒆𝒅 𝒃𝒚 𝑨)
= (14 + 16 + 10 + 10)/4
= 50/4
= 12.5

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.Let’s find the Mean and Median for both data

Consider this data collected from a survey of a colony. Choose an appropriate scale and draw a double-bar graph. Write down your observations.While drawing a bar graph, we follow these steps
1. First we decide what to put in x-axis and y-axis
We always use numbers in y-axis, so Number of people is in y-aixs
And, Favourite sport are in y-axis
2. Then, we find out our Scale
We can take multiples of 100
Thus, scale is 1 unit length = 100 people
3. Lastly, we decide our legend – color to denote
We choose blue for Watching, Red for Participating

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?In statistics, whenever you want to cut a population in half (50% vs 50%), you always use the Median. If you want to find the "average height," you use the Mean.

Describe the mean and median of heights of your class. You can visualise the heights on a dot plot.Let’s consider the data like this
101, 102, 106, 109, 110, 110, 112, 115, 115, 115, 115, 115, 117, 120, 120, 123, 125

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.Our answer is
(d) The mean height of students in the other section cannot be determined.
Because if one class has a specific average height doesn't force the other class to be the same. The other class might have taller students or shorter students purely by chance. They are separate groups of people.

(a) Standing tall in the storm. (a) Write estimated values for the number of skyscrapers in New York, Tokyo, and London. Our estimation is
New York: around 280
Tokyo: around 165
London: around 35
Question 8 (b) Standing tall in the storm. (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. (i) Valid. (Count bars above Mumbai: there are 12).
(ii) Valid. (Count bars below Mumbai: there are 7).
(iii) Invalid. This chart shows the number of skyscrapers, not which building is the tallest in the world.

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.From measurement, our data came out to be
Average Difference:
To find the average "error" in my guesses, I add up all the differences and divide by the number of objects (5)
Thus,
Average difference = (𝑆𝑢𝑚 𝑜𝑓 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒)/(𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑜𝑏𝑗𝑒𝑐𝑡𝑠)
= (2.5 + 0.5 + 1.0 + 2.5 + 3.0)/5
= 9.5/5
= 1.9 cm

(a) 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.Now, our data is
Week 1: 410, 400, 370, 340, 360, 400, 320, 330, 310
Week 2: 320, 290, 380, 280, 270, 230, 220, 240

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:I will choose option (b) about Classmate Names because it has fun data to analyze!
Step 1: Collect Data (Simulated Classmates)
Let's pretend these are the names of 15 students in your class:
Aarav, Vivaan, Aditi, Vihaan, Arjun, Sai, Reyansh, Aaryan, Krishna, Ishaan, Sara, Ananya, Diya, Rohan, Pari.

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. Since these are long-term projects, I will give you a "Cheat Sheet" on how the data might look so you know what to aim for.
Simulated Data (14 days):
2, 3, 1, 0, 4, 2, 2, 5, 1, 0, 2, 3, 1, 2

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 m-any 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. Since these are long-term projects, I will give you a "Cheat Sheet" on how the data might look so you know what to aim for.