# Data Interpretation - Table Charts

Exercise : Table Charts - Table Chart 7
Directions to Solve

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 Exams 28 23 17 27 Students failed in half-yearlybut passed in Annual Exams 14 12 8 13 Students passed in half-yearlybut failed in Annual Exams 6 17 9 15 Students passed in both Exams 64 55 46 76

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?
Half yearly examinations were more difficult.
Annual examinations were more difficult.
Both the examinations had almost the same difficulty level.
The two examinations cannot be compared for difficulty level.
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?
336
189
335
430
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 Section
B Section
C Section
D Section
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 Section
B Section
C Section
D Section
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

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 section
B section
C section
D section
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

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.