Class 9 Ganita Manjari • Chapter 10
📖 Textbook Reference: 10.2 Visualising and Interpreting Data
A 100% stacked bar chart shows the proportion (percentage) of categories inside a group, not the absolute numbers.
By forcing every bar to stretch to 100%, we can easily compare how fractions shrink or grow across different groups (like age brackets) without being distracted by differences in total population size.
11. Look at the following graph. What do you notice? What do you wonder? Write your inferences.
1
A 100% stacked bar chart compares the proportion (percentage) of different categories within a group, not the absolute numbers of people.
2
To infer trends, track how a specific color block expands or shrinks as you move down through the different age groups.
1
Look at the blue bar (Seeing). What happens to its width as people get older (moving from the top bar to the bottom bar)?
2
Look at the green bar (Movement). Is it wider in young people or older people?
3
Look at the yellow (Speech) and purple (Mental Retardation) bars. In which age group are these fractions the largest?
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Assuming Absolute Numbers: A common mistake is saying, "Because the blue bar is 25% for 60+ and only 18% for 0-19, there are more blind old people than blind young people." This chart does not show total population size! It only shows that within their own age group, sight issues make up a larger percentage of the problems for the elderly.
Visual Inferences
Q: Look at the graph. What do you notice? What do you wonder? Write your inferences.
By tracking how the colored bands change width across the age groups, we can make the following clear inferences:
1. Movement & Aging
The green bar (Movement disability) gets noticeably wider as age increases. It is a much larger fraction of disabilities in the 40-59 and 60+ groups compared to the youngest group. This makes sense as joints and bones weaken with age.
2. Vision & Aging
The blue bar (Seeing disability) shrinks slightly in middle age, but then expands to become the largest single fraction (~25%) in the 60+ age group. This aligns with elderly populations developing cataracts and vision loss.
3. Early-Life Disabilities
The yellow bar (Speech) and purple bar (Mental Retardation) are at their widest in the 0-19 age group. These proportions shrink significantly in older age groups. This suggests these conditions are often congenital (present from birth) or identified early in childhood.
12. Individual project: Do at least one of the following.
(i) Recall the previous day and fill in the approximate time spent lying down, sitting, and standing/moving around, etc. Ask at least 2 of your family members about their day and fill it in. Visualise it using a stacked bar chart. Discuss with your class how you arrived at the estimated time spent in each state.
(ii) Visualise your family's monthly expenditure using a 100% stacked bar chart.
(i) Recall the previous day and fill in the approximate time spent lying down, sitting, and standing/moving around, etc. Ask at least 2 of your family members about their day and fill it in. Visualise it using a stacked bar chart. Discuss with your class how you arrived at the estimated time spent in each state.
(ii) Visualise your family's monthly expenditure using a 100% stacked bar chart.
Project Steps
Step 1: Collect Data
For Part (i), ask two family members for their daily hours. Ensure all rows add to 24. For Part (ii), group expenses (Food, Rent, Bills).
Step 2: Calculate %
Divide the specific amount by the total base (24 hours, or Total Monthly Budget), then multiply by 100 to get the exact percentage.
Step 3: Draw the Chart
Draw a single 100% width bar for each person/budget. Use a ruler to mark the percentages calculated in Step 2. Use distinct colors.
1
Applying stacked charts to real life helps track how a fixed total limit (like 24 hours in a day, or a set monthly budget) is divided up.
1
Hint for (i): Be careful that your hours add up to exactly 24. A good way to estimate is to write down the time you wake up and the time you go to bed.
2
Hint for (ii): Since expenses change every month, use an average month. Group small expenses together into an "Other" category to keep the chart clean.
!
Mathematical Errors: The most common mistake in these projects is drawing a 100% stacked bar chart where the percentages calculated don't actually add up to 100, or creating a time chart for a person that adds up to 26 hours. Always double-check your addition!
Sample Project Guide
Q: Recall the previous day and fill in the approximate time spent lying down, sitting, and moving. Visualise it.
Here is a sample framework of how a student might complete Project (i):
1. Estimating the Data (My Day):
Lying down: I slept from 10 PM to 6 AM (8 hours). I rested on the couch for 1 hour. Total = 9 hours.
Sitting: I was at school for 6 hours, did homework for 2 hours, and ate meals for 1 hour. Total = 9 hours.
Moving: Playing sports, walking to school, and chores took the remaining time. Total = 6 hours.
Check: $9 + 9 + 6 = 24$ hours. Perfect!
2. Converting to Percentages for the Chart:
Lying down: $\frac{9}{24} \times 100 = 37.5\%$
Sitting: $\frac{9}{24} \times 100 = 37.5\%$
Moving: $\frac{6}{24} \times 100 = 25.0\%$
Check: $37.5 + 37.5 + 25 = 100\%$.
Now, simply draw a 10cm bar on paper (where 1cm = 10%). Color the first 3.75cm Blue, the next 3.75cm Red, and the final 2.5cm Green! Do this for your family members and stack them vertically.
