Question

The given figure represents the percentage of marks on X-axis and the number of students on Y-axis. Find the number of students who scored less than or equal to \(50 \%\) of marks. (1) 35 (2) 15 (3) 20 (4) 30

Short answer

Options: (1) 35 (2) 15 (3) 20 (4) 30

Step-by-step solution

Locate the 50% marks point on the X-axis

In the figure, find the point on the X-axis that corresponds to \(50 \%\) of marks. This point will act as a reference for determining the number of students with marks less than or equal to \(50 \%\).

Identify the relevant bars in the figure

Now, identify the bars in the figure whose marks range includes values less than or equal to \(50 \%\). These bars will help us find the total number of students who scored less than or equal to \(50 \%\).

Sum the number of students from the relevant bars

For each bar identified in Step 2, locate the corresponding number of students on the Y-axis. Add these numbers together to get the total number of students who scored less than or equal to \(50 \%\) of marks.

Compare the result with the given options

Finally, compare the total number of students found in Step 3 with the given options (1) 35, (2) 15, (3) 20, and (4) 30. The correct option will be the one that matches the total number of students from our calculation.

Key concepts

Data Representation

Understanding data representation, specifically through bar graphs, is essential for interpreting complex information easily. Bar graphs display data with rectangular bars, where the length or height of each bar is proportional to the value it represents. This visual mechanism can quickly convey comparative numbers among different groups or categories, making data easier to digest and analyze.

For example, in an educational context, a bar graph might be used to represent the relationship between student scores and the number of students achieving those scores. Along the X-axis (the horizontal part of the graph), you'll find percentages or scores; the Y-axis (the vertical part) shows the number of students. The intersection of the X and Y axes helps in identifying specific values rapidly and accurately. This graphical approach simplifies the extraction of valuable insights from numerical data, aiding students in recognizing patterns and drawing conclusions.

Percentage Calculation

Percentage calculation plays a key role in interpreting data, especially when it comes to understanding proportions or making comparisons. Grasping the concept of percentages is crucial since it's used to describe how large or small one quantity is, relative to another. When you see a percentage, it tells you how many parts per hundred are being considered.

For instance, if a student has scored 50% on a test, it means the student has achieved 50 out of 100 possible points. This percentage becomes particularly useful when analyzing bar graphs because it allows for comparison across different categories or groups. When faced with a problem involving percentages in a graphical context, one should first locate the percentage in question on the appropriate axis e.g. 50% on the X-axis if discussing marks, then interpret the corresponding data on the other axis.

Math Problem Solving

Math problem solving is the process of understanding and tackling mathematical challenges, step by step. It begins with interpreting the problem, planning the steps, carrying out calculations, and verifying the results. A good approach is to break down the problem into smaller, manageable parts and address each part systematically.

In the context of the given bar graph exercise, problem-solving involves several steps. First, determining the data point of interest (e.g., 50% mark), then identifying all relevant data bars that align with or fall below this threshold. The next step would include the addition of numerical values found on the Y-axis corresponding to the identified bars to calculate the total count. Lastly, verifying the calculated total against provided options requires careful consideration to ensure accuracy. This methodical approach ensures that students can tackle problems with clarity and precision, enhancing their learning outcomes and boosting their confidence in math.