Data Interpretation - Table Charts

A school has four sections A, B, C, D of Class IX students.

The results of half yearly and annual examinations are shown in the table given below.

Result No. of Students
Section A Section B Section C Section D
Students failed in both Exams28231727
Students failed in half-yearly
but passed in Annual Exams
1412813
Students passed in half-yearly
but failed in Annual Exams
617915
Students passed in both Exams64554676

1. 

If the number of students passing an examination be considered a criteria for comparision of difficulty level of two examinations, which of the following statements is true in this context?

A. Half yearly examinations were more difficult.
B. Annual examinations were more difficult.
C. Both the examinations had almost the same difficulty level.
D. The two examinations cannot be compared for difficulty level.

Answer: Option C

Explanation:

Number of students who passed half-yearly exams in the school

  = (Number of students passed in half-yearly but failed in annual exams)

      + (Number of students passed in both exams)

  = (6 + 17 + 9 + 15) + (64 + 55 + 46 + 76)

  = 288.

Also, Number of students who passed annual exams in the school

  = (Number of students failed in half-yearly but passed in annual exams)

      + (Number of students passed in both exams)

  = (14 + 12 + 8 + 13) + (64 + 55 + 46 + 76)

  = 288.

Since, the number of students passed in half-yearly = the number of students passed in annual exams. Therefore, it can be inferred that both the examinations had almost the same difficulty level.

Thus Statements (a), (b) and (d) are false and Statement (c) is true.


2. 

How many students are there in Class IX in the school?

A. 336
B. 189
C. 335
D. 430

Answer: Option D

Explanation:

Since the classification of the students on the basis of their results and sections form independent groups, so the total number of students in the class:

= (28 + 23 + 17 + 27 + 14 + 12 + 8 + 13 + 6 + 17 + 9 + 15 + 64 + 55 + 46 + 76)

= 430.


3. 

Which section has the maximum pass percentage in at least one of the two examinations?

A. A Section
B. B Section
C. C Section
D. D Section

Answer: Option D

Explanation:

Pass percentages in at least one of the two examinations for different sections are:

For Section A [ (14 + 6 + 64) x 100 ] % = [ 84 x 100 ] % = 75%.
(28 + 14 + 6 + 64) 112

For Section B [ (12 + 17 + 55) x 100 ] % = [ 84 x 100 ] % = 78.5%.
(23 + 12 + 17 + 55) 107

For Section C [ (8 + 9 + 46) x 100 ] % = [ 63 x 100 ] % = 78.75%.
(17 + 8 + 9 + 46) 80

For Section D [ (13 + 15 + 76) x 100 ] % = [ 104 x 100 ] % = 79.39%.
(27 + 13 + 15 + 76) 131

Clearly, the pass percentage is maximum for Section D.


4. 

Which section has the maximum success rate in annual examination?

A. A Section
B. B Section
C. C Section
D. D Section

Answer: Option A

Explanation:

Total number of students passed in annual exams in a section

= [ (No. of students failed in half-yearly but passed in annual exams)

        + (No. of students passed in both exams)

   ] in that section

Therefore Success rate in annual exams in Section A

    = [ No. of students of Section A passed in annual exams x 100 ] %
Total number of students in Section A

    = [ (14 + 64) x 100 ] %
(28 + 14 + 6 + 64)

    = [ 78 x 100 ] %
112

    = 69.64%.

Similarly, success rate in annual exams in:

Section B [ (12 + 55) x 100 ] % = [ 67 x 100 ] % = 62.62%.
(23 + 12 + 17 + 55) 107

Section C [ (8 + 46) x 100 ] % = [ 54 x 100 ] % = 67.5%.
(17 + 8 + 9 + 46) 80

Section D [ (13 + 76) x 100 ] % = [ 89 x 100 ] % = 67.94%.
(27 + 13 + 15 + 76) 131

Clearly, the success rate in annual examination is maximum for Section A.


5. 

Which section has the minimum failure rate in half yearly examination?

A. A section
B. B section
C. C section
D. D section

Answer: Option D

Explanation:

Total number of failures in half-yearly exams in a section

= [ (Number of students failed in both exams)

        + (Number of students failed in half-yearly but passed in Annual exams)

   ] in that section

Therefore Failure rate in half-yearly exams in Section A

    = [ Number of students of Section A failed in half-yearly x 100 ] %
Total number of students in Section A

    = [ (28 + 14) x 100 ] %
(28 + 14 + 6 + 64)

    = [ 42 x 100 ] %
112

    = 37.5%.

Similarly, failure rate in half-yearly exams in:

Section B [ (23 + 12) x 100 ] % = [ 35 x 100 ] % = 32.71%.
(23 + 12 + 17 + 55) 107

Section C [ (17 + 8) x 100 ] % = [ 25 x 100 ] % = 31.25%.
(17 + 8 + 9 + 46) 80

Section D [ (27 + 13) x 100 ] % = [ 40 x 100 ] % = 30.53%.
(27 + 13 + 15 + 76) 131

Clearly, the failure rate is minimum for Section D.