Class 9 Ganita Manjari • Chapter 10
📖 Textbook Reference: 10.2 Visualising and Interpreting Data
Stacked bar charts show us two things simultaneously: the Grand Total (the very top of the bar) and the Individual Parts (the colored layers).
When comparing absolute growth over time, look at the overall height. When comparing relative "share", look at how thick one layer is compared to the whole stack.
7. Answer the following questions based on the graph.
(i) In 2003, approximately how many total objects were found orbiting Earth in space? In what year did this number double?
(ii) Find the approximate number and share of payload objects and other objects in the year 2025.
(iii) What can you say about the number of payload objects over time, and the number of other objects over time? What can you say about the share of payload objects over time, and the share of other objects over time?
(i) In 2003, approximately how many total objects were found orbiting Earth in space? In what year did this number double?
(ii) Find the approximate number and share of payload objects and other objects in the year 2025.
(iii) What can you say about the number of payload objects over time, and the number of other objects over time? What can you say about the share of payload objects over time, and the share of other objects over time?
1
To find absolute numbers, trace the top of the bar straight to the Y-axis.
2
To find the "share" or percentage, look at how thick the specific colored layer is compared to the entire stack.
1
For (i): Look at the column for 2003. Trace the top of the stack to the Y-axis. What number does it hit? Then scan the graph to the right to see where that total height doubles.
2
For (ii): Go to 2025. First, find the total height. Then estimate the thickness of the green part (Payload) and the teal part (Other).
3
For (iii): Look at the green part. Is it just getting taller, or is it taking up a much larger percentage of the total stack today than it did in 1990?
!
Confusing Total Growth with Share Growth: A common mistake is saying "The share of Other Objects is increasing." While the absolute number of Other Objects is increasing, their percentage share of the total pie is actually shrinking because Payload objects are growing so rapidly!
Step-by-Step Analysis
Q(i): In 2003, approximately how many total objects were found orbiting Earth in space? In what year did this number double?
Looking at the 2003 column, the top of the bar aligns perfectly with the 10,000 gridline.
If we look for the year where the total hits 20,000 (double 10,000), we trace to the 2020 column.
Ans: Approx 10,000 objects in 2003. It doubled around 2020.
Q(ii): Find the approximate number and share of payload objects and other objects in the year 2025.
In 2025, the total height is roughly 33,000.
The Payload (green) portion is roughly 13,000 objects. (This is about 40% of the total).
The Other (teal) portion is roughly 20,000 objects. (This is about 60% of the total).
Ans: Payload: ~13,000 (~40% share). Other: ~20,000 (~60% share).
Q(iii): What can you say about the number/share of payload and other objects over time?
Absolute Numbers: Both Payload and Other objects are increasing rapidly over time.
Share: In the past, Payload objects were a tiny sliver of the total. Recently, the green segment has exploded in thickness. Therefore, the share of Payload objects is increasing dramatically, while the relative share of Other objects is decreasing.
8. Observe the following infographic. What Percentage of Schools have a Playground?
(i) Identify the correct inference(s) from the statements given.
(a) More schools have a playground in Haryana compared to Uttarakhand.
(b) Approximately every 2 out of 3 schools in Arunachal Pradesh have a playground.
(c) Punjab has the highest number of schools with a playground.
(d) Suppose it is given that Maharashtra has more schools than Telangana. Then the number of schools having a playground is more in Maharashtra.
(ii) Using the information given, can we find the nation-wide percentage of schools with a playground? If not, what additional information is needed?
(i) Identify the correct inference(s) from the statements given.
(a) More schools have a playground in Haryana compared to Uttarakhand.
(b) Approximately every 2 out of 3 schools in Arunachal Pradesh have a playground.
(c) Punjab has the highest number of schools with a playground.
(d) Suppose it is given that Maharashtra has more schools than Telangana. Then the number of schools having a playground is more in Maharashtra.
(ii) Using the information given, can we find the nation-wide percentage of schools with a playground? If not, what additional information is needed?
State Analytics Dashboard
Haryana
90%
Uttarakhand
78%
Arunachal Pradesh
68%
Punjab
98%
Maharashtra
93%
Telangana
74%
1
A high percentage does not guarantee a high absolute number. It completely depends on the base total.
2
For example: 90% of 10 schools is just 9 schools. But 10% of 10,000 schools is 1,000 schools!
1
Hint for (i)(a) & (c): Do you know the absolute total number of schools in Haryana or Punjab? If not, can you claim they have the most absolute playgrounds?
2
Hint for (i)(b): What is 2 divided by 3 as a percentage? Does it match the dashboard?
3
Hint for (i)(d): Maharashtra has a higher percentage (93%) AND a larger base number of schools. If both the base and the multiplier are bigger, what must be true about the final answer?
!
The Percentage Trap: Assuming that because Punjab has the highest rate (98%), it automatically has the highest absolute number of playgrounds. If Uttar Pradesh has 100,000 schools at a 76% rate, it dwarfs Punjab's absolute numbers!
Logical Inferences
Q(i): Identify the correct inference(s) from the statements given.
(a) False. We know Haryana has a higher rate (90% vs 78%), but we don't know the absolute total number of schools. Uttarakhand might have vastly more schools.
(b) True. 2 out of 3 is $\frac{2}{3} \approx 66.67\%$. The dashboard shows Arunachal Pradesh at 68%, which is approximately 2 out of 3.
(c) False. Punjab has the highest rate, but not necessarily the highest absolute number.
(d) True. If Maharashtra has a higher rate (93% vs 74%) AND a larger total base of schools, then mathematically it must have a higher absolute number of playgrounds.
Q(ii): Can we find the nation-wide percentage of schools with a playground? If not, what additional information is needed?
We cannot calculate the nation-wide percentage from this data alone.
Because the total number of schools varies drastically by state, we cannot simply average the percentages together. We need the weights.
Ans: No. We need the total absolute number of schools in each state to calculate the weighted average.
