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Class 9 Ganita Manjari • Chapter 10
📖 Textbook Reference: A Typical Day
A stacked bar chart usually hides differences in the total amounts between groups.[cite: 2]
The Exception: When measuring how people spend a "Day", the total amount is exactly the same for everyone: exactly 24 hours. Because the total is the same for every person, a 100% stacked bar chart works exactly like a regular stacked bar chart![cite: 2]
You can match $100\%$ directly to $24\text{ hours}$, and $50\%$ directly to $12\text{ hours}$, without making any math errors.[cite: 2]
1. The smart watch data of 5 people was tracked from Monday to Friday. The recorded data tells us how many hours each person spent lying down, sitting, and standing or moving around, etc., as shown in the following table.[cite: 2]
(i) How much time does Sahana spend per day in each of these body-states? Make a reasonable guess and fill her row in the table.
(ii) Guess what activity or work Julie could be engaged in based on the data. Find out what your classmates' guesses are.
(iii) Complete the chart below based on the tabular data.[cite: 2]
(i) How much time does Sahana spend per day in each of these body-states? Make a reasonable guess and fill her row in the table.
(ii) Guess what activity or work Julie could be engaged in based on the data. Find out what your classmates' guesses are.
(iii) Complete the chart below based on the tabular data.[cite: 2]
| Lying down | Sitting | Standing or Moving around etc. |
|
|---|---|---|---|
| Pavani (Patient) | 20 | 3 | 1 |
| Raghu (Nurse) | 7 | 4 | 13 |
| Zakir (Teacher) | 8 | 6 | 10 |
| Sahana (Student) | ___ | ___ | ___ |
| Julie (__________) | 8 | 10 | 6 |
1
Every person has exactly 24 hours in a day.
2
So, 100% of the bar is always 24 hours. This means we can easily change hours into percentages.
1
Hint for (i): A student sleeps for about 8 hours. Think about how many hours you sit in school and do homework. The rest of the 24 hours is for moving and playing.
2
Hint for (ii): Look at Julie's numbers. She sits for 10 hours. What kind of job makes you sit at a desk for 10 hours?
!
Wrong Total Hours: The numbers in Sahana's row must add up to exactly 24. A common mistake is writing numbers that add up to more or less than 24.
Simple Answers
Solution (i): Sahana's Data
A good guess for a student is 8 hours of sleep (Lying down). School and study take about 9 hours (Sitting).
The rest is $24 - 8 - 9 = 7$ hours for sports and moving.
Ans: Lying: 8h, Sitting: 9h, Moving: 7h.
Solution (ii): Julie's Job
Julie sits for a very long time (10 hours) and sleeps for 8 hours.
Ans: Julie might have a desk job, like a software engineer, writer, or bank clerk.
Solution (iii): Drawing the Chart
To draw the bars, remember that 24 hours equals 100%.
For Julie: Draw Gray for 8 hours, Red for 10 hours, and Blue for 6 hours. They will fit perfectly in the blank box.
Suppose another person, David (Athlete), was added to the table. He sleeps for 9 hours and trains for 12 hours a day. How much space would his red "Sitting" block take up on the chart?
1
First, find the remaining hours using the 24-hour rule. Then, change those hours into a percentage.
1
Total day = 24 hours.
2
Lying down = 9 hours. Moving = 12 hours.
3
Subtract those from 24 to find his sitting hours.
4
What percentage of 24 is that answer?
!
Thinking that 1 hour is 1% on the chart. It is not! A full 100% chart is 24 hours. So, 1 hour is about 4.16% of the chart space.
Easy Steps
Total used time = $9\text{ hours (Lying)} + 12\text{ hours (Moving)} = 21\text{ hours}$.
Remaining sitting time = $24 - 21 = 3\text{ hours}$.
Change to Percentage:
Percentage = $\frac{3}{24} \times 100 = \frac{1}{8} \times 100 = 12.5\%$.
Ans: His red sitting block will take exactly 12.5% of the chart space.
Look at the chart. Who spends the most hours Standing or Moving around?
A Pavani
B Raghu
C Zakir
D Julie
1
Because this chart shows a 24-hour day for everyone, a wider color block always means more hours.
Visual Check
Look at the blue blocks (Standing/Moving) on the chart.
Raghu's blue block is very wide, showing $13$ hours of movement.[cite: 2]
This makes sense because a nurse spends most of the day walking to help patients.
Ans: Option (B)
In this specific chart, we can easily compare Pavani and Zakir's hours by looking at the block sizes. Why could we not do that for Fatima and Naveen's flowers in the earlier chapter?
A Because hours are whole numbers, and flowers are not.
B Because every person has exactly 24 hours, but the flower totals were different.[cite: 2]
C Because there are 5 people in this chart, which makes it better.
D We actually cannot compare Pavani and Zakir's hours.
1
A percentage is just a part of a total. If the totals are very different, the parts cannot be compared. If the totals are exactly the same, you can easily compare the parts.
Simple Explanation
Every human has exactly $24$ hours in a day.
Because the total time for Pavani is $24$ hours, and the total time for Zakir is $24$ hours, the sizes of their blocks can be compared directly.[cite: 2]
For example, $50\%$ of Pavani's day is $12$ hours. $50\%$ of Zakir's day is also $12$ hours.
Ans: Option (B)
