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class 9 ganita manjari chapter 10
📖 Textbook Reference: What does the 100% stacked bar tell us?
When a 100% stacked bar represents a universal constant—like the $24$ hours in a day—it behaves as both a 100% stacked bar *and* an absolute stacked bar simultaneously!
Because everyone's day is exactly $24$ hours long, a larger percentage directly translates to a larger absolute amount of time. You don't have to worry about hidden baselines.
However, looking *only* at the overall national average hides the massive differences and nuances within specific sub-groups (like age or gender). Grouping the data allows us to discover deeper trends.
Example 9: The charts below show the time spent on different activities in a typical $24$-hour day by Indians (data from the National Time Use Survey). The first chart shows the overall average. The second chart groups the exact same data by age.
Think and Reflect:
1. Do you remember the sleep time trend over age? Does it align here?
2. Why does learning time drop significantly for the 15-24 age group compared to 6-14?
3. Do adults spend about an equal amount of time in paid and unpaid work?
Think and Reflect:
1. Do you remember the sleep time trend over age? Does it align here?
2. Why does learning time drop significantly for the 15-24 age group compared to 6-14?
3. Do adults spend about an equal amount of time in paid and unpaid work?
1
When plotting time across a 24-hour day, a standard stacked bar and a 100% stacked bar are visually identical! This is because everyone's "total pie" is exactly the same: 24 hours.
2
Grouping data by specific attributes (like Age) reveals important nuances that the overall "Average" completely hides.
1
Hint for Q1: Track the Green block (Sleep) from left to right across the four age groups. Does it go down and then up?
2
Hint for Q2: The Grey block (Learning) drops from $22\%$ in Children to $11\%$ in Youth, and vanishes for Adults. What major life transition happens around ages 18-22?
3
Hint for Q3: Look at the Adult column. Compare the Purple block (Paid) to the Pink block (Unpaid). Are the numbers similar? Does this represent a single person's day, or a massive average?
!
The "Average Person" Trap: Looking at the Adult column, you might conclude "Ah, the typical 35-year-old works a 3-hour paid job and does 3 hours of unpaid chores." That is false! This is an average across hundreds of millions of people. It heavily blends traditional gender roles (men doing 8+ hours of paid work, women doing 8+ hours of unpaid care work) into a "middle" number that represents almost nobody perfectly.
Analysis & Answers
Q1: Sleep Time Trend
Tracking the green block: Children ($38\%$) sleep the most. Sleep drops during Youth ($34\%$) and hits its lowest in Adults ($32\%$). It then rises again for the Elderly ($37\%$). This "U-shape" perfectly matches general biological and lifestyle trends.
Q2: Drop in Learning Time
Children ($6-14$) spend $22\%$ of their time learning because school is compulsory. Youth ($15-24$) spend only $11\%$. This happens because many youths finish high school and transition out of formal education and into the workforce (notice Paid Work jumping to $7\%$).
Q3: Paid vs Unpaid Work in Adults
According to the chart, the *average* adult spends roughly equal time on Paid Work ($14\%$) and Unpaid Work ($15\%$). However, this average likely masks massive disparities, especially regarding gender roles where women disproportionately shoulder unpaid care work while men do paid work.
Based on the "Time use by age group" chart, which age group experiences the largest sudden increase in Leisure, Social & Travel time?
A. From Children to Youth
B. From Youth to Adults
C. From Adults to Elderly
D. Leisure time steadily decreases with age.
1
Locate the yellow block (Leisure, Social & Travel) and track its percentage values across the four columns.
Visual Tracking
Children: $26\%$
Youth: $26\%$
Adults: $26\%$
Elderly: $33\%$
Leisure time remains perfectly flat through childhood and the working years, and only spikes upwards significantly when people reach retirement age (Elderly).
Ans: Option (C)
Why does the "Average Indian" chart (the single column on the left) have a single vertical stacked bar that perfectly matches the right Y-axis (which measures 0h to 24h)?
A. Because 100% of Indians were surveyed.
B. Because the absolute total for every single person's day is exactly 24 hours. Therefore, a 100% stacked bar mapping to a 24h axis is mathematically perfect.
C. Because the average Indian sleeps exactly 10 hours.
D. It is a visual error; stacked bars cannot represent time.
1
The critical flaw of a 100% stacked bar chart is that it hides differences in the absolute total.
2
However, when measuring a "Day", the absolute total is a universal constant (24 hours). Therefore, the flaw disappears!
Logical Breakdown
Unlike the garden example (where Fatima might have $10$ flowers and Naveen $5000$), here every single person has exactly $24$ hours in their day.
Because the "Total" is identical for everyone, a 100% stacked bar chart functions exactly like an absolute stacked bar chart.
You can map $100\%$ directly to $24\text{h}$, and $50\%$ directly to $12\text{h}$, without losing any mathematical accuracy.
Ans: Option (B)
