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Question

A school has four sections A, B, C, D of Class IX students.
ResultSection ASection BSection CSection D
Students failed in both exams28231727
Students failed in half-yearly but passed in annual exams1412813
Students passed in half-yearly but failed in annual exams617915
Students passed in both exams64554676
In the context of comparing the difficulty level of the two examinations based on the number of students passing, which of the following statements is true?

The correct answer is
Both the exams had almost the same difficulty level.

Class IX Exam Difficulty Comparison

To compare the difficulty levels of the Half-yearly and Annual examinations, we analyze the total number of students who passed or failed each exam across all sections (A, B, C, D).

Student Performance Data for Exam Comparison

Category Section A Section B Section C Section D Total
Students failed in both exams 28 23 17 27 95
Students failed in half-yearly, passed annual 14 12 8 13 47
Students passed half-yearly, failed annual 6 17 9 15 47
Students passed in both exams 64 55 46 76 241
Total Students Per Section 112 107 80 131 430

Pass and Fail Counts Analysis

We aggregate the counts to compare the performance in each exam:

  • Total students passing Half-Yearly Exam = (Passed Half-Yearly, Failed Annual) + (Passed Both)
    = 47 + 241 = 288 students.
  • Total students passing Annual Exam = (Failed Half-Yearly, Passed Annual) + (Passed Both)
    = 47 + 241 = 288 students.
  • Total students failing Half-Yearly Exam = (Failed Both) + (Failed Half-Yearly, Passed Annual)
    = 95 + 47 = 142 students.
  • Total students failing Annual Exam = (Failed Both) + (Passed Half-Yearly, Failed Annual)
    = 95 + 47 = 142 students.

Exam Difficulty Conclusion

The total number of students who passed the Half-yearly exam (288) is identical to the total number who passed the Annual exam (288). Likewise, the total number of students who failed the Half-yearly exam (142) is the same as the total number who failed the Annual exam (142). This consistency in outcomes indicates that both examinations had approximately the same difficulty level.

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Important Questions from Tabulation

  1. What is the ratio of total number of patients recovered from covid-19 in April to total number of patients recovered from covid-19 in March?

  2. In which state, the number of patients who recovered from covid-19 steadily decreasing?

  3. What is the average number of patients who recovered from Covid-19 in Madhya Pradesh in four months?

  4. Find the difference between the total number of patients recovered from Covid-19 in all months in Punjab and the total number of patients recovered from Covid-19 in all months in Rajasthan.

  5. In February 2021 the number of patients recovered from Covid-19 in Punjab is how much approximant percent more/less than the number of patients recovered from Covid-19 Uttar Pradesh in the same month?

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