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Class 9 Ganita Manjari • Chapter 10
📖 Textbook Reference: 10.2 Visualising and Interpreting Data
There are multiple ways to cluster data depending on the primary focus of the comparison.[cite: 2]
Choice 1: Clustering by Category. This groups families together under "Housing" or "Food". It makes it very easy to compare how different families behave within a single expense category.
Choice 2: Clustering by Family. This groups all the different expenses of a single family together. It makes it very easy to compare which category a specific family spent the most or least on.
Answer the following questions based on the charts below. Try to answer each question by looking at Choice 1 first, and then Choice 2. Which was easier?
1. Which family spent the least on housing?
2. Which family spent the most on healthcare?
3. Approximately how much did Family A spend on education?
4. Which category did Family B spend most on?
5. Did Family A spend more on food or on healthcare?[cite: 2]
1. Which family spent the least on housing?
2. Which family spent the most on healthcare?
3. Approximately how much did Family A spend on education?
4. Which category did Family B spend most on?
5. Did Family A spend more on food or on healthcare?[cite: 2]
1
The choice of the cluster-column chart depends entirely on your primary focus.
2
If you are comparing different families inside a single category (like Housing), the left chart (Choice 1) is better because all families' housing bars are grouped together.
3
If you are comparing different categories inside a single family (like Family A's overall budget), the right chart (Choice 2) is better because all of Family A's bars are grouped together.
1
Q1 (Least on housing): Look at the left chart. Find the "Housing" cluster. Which bar is lowest?
2
Q2 (Most on healthcare): Look at the left chart. Find the "Healthcare" cluster. Which bar is highest?
3
Q3 (Fam A Edu): Look at either chart. Find the bar for Family A's Education. What number does it align with on the y-axis?
4
Q4 (Fam B spend most): Look at the right chart. Find the "Family B" cluster. Which color bar is highest? What does that color represent?
5
Q5 (Fam A Food vs Health): Look at the right chart under "Family A". Compare the Food bar to the Healthcare bar. Which is taller?
!
Looking at the wrong chart: Trying to figure out "Which category did Family B spend most on?" using the left chart forces you to scan your eyes across 6 completely different places on the graph to find the tallest blue bar! Always choose the chart that logically groups your target data together.
Answers and Chart Selection
Q1: Which family spent the least on housing?
Looking at the "Housing" cluster in Choice 1, the brown bar is the shortest.
Ans: Family C (Choice 1 is easier).
Q2: Which family spent the most on healthcare?
Looking at the "Healthcare" cluster in Choice 1, the orange bar is the tallest.
Ans: Family A (Choice 1 is easier).
Q3: Approx how much did Family A spend on education?
Locate the Family A Education bar on either chart and trace it to the y-axis. It sits roughly halfway between 1000 and 1500.
Ans: ~1300 rupees (Exactly 1280) (Both are okay).
Q4: Which category did Family B spend most on?
Looking at the "Family B" cluster in Choice 2, the red bar is the tallest. The legend says red is Housing.
Ans: Housing (Choice 2 is easier).
Q5: Did Family A spend more on food or healthcare?
Looking at the "Family A" cluster in Choice 2, the purple bar (Healthcare) is taller than the blue bar (Food).
Ans: Healthcare (Choice 2 is easier).
Based on the provided charts, did Family C spend more on Transportation or Education? Which chart makes this easier to answer?
1
When comparing two different categories within the same family, you want the chart that groups data by family.
1
Look at the Right Chart (Choice 2). Find the cluster labeled "Family C".
2
Compare the height of the Transportation bar (Green) to the Education bar (Yellow).
!
If you try to use the Left Chart, you have to find the brown bar in the Education cluster, mentally hold its height, then jump across the graph to find the brown bar in the Transportation cluster. This is visually confusing and error-prone!
Visual Analysis
Looking at Choice 2 (the right chart), we can directly compare the bars inside Family C's cluster.
The yellow bar (Education) is clearly taller than the green bar (Transportation).
Ans: Family C spent more on Education. Choice 2 makes it easier.
If you want to quickly identify which family spends the absolute minimum amount on Recreation, which chart layout is most efficient?
A Choice 1 (Clustered by Categories)
B Choice 2 (Clustered by Families)
C Both are equally efficient.
D Neither, a pie chart is required.
1
When finding a max or min across different families for a single category, the chart grouped by category is best.
Logical Explanation
In Choice 1, all the Recreation bars for Family A, B, and C are clustered right next to each other. You can instantly see that Family B's bar is missing (zero).
In Choice 2, you would have to scan the grey bars across three separate clusters to compare them, which takes longer.
Ans: Option (A)
Look at Family C's expenditure in the "Food" category on the charts. Which other family spent the exact same amount on Food?
A Family A
B Family B
C Both Family A and B
D None, Family C spent the most.
1
Use Choice 1 (clustered by categories) and look specifically at the "Food" cluster to compare the heights of the three bars.
Visual Observation
In the Left Chart (Choice 1), locate the "Food" cluster.
You will notice that the Orange bar (Family A) and the Brown bar (Family C) are exactly the same height.
This indicates that Family A and Family C spent the identical amount on food ($1700\text{ Rs}$ each).
Ans: Option (A)
