Question

Marks obtained by 200 students in an examination are given below: Draw an ogive for the given distribution taking 2 cm = 10 marks on one axis and 2 cm = 20 students on the other axis. Using the graph, determine

(i) The median marks.

(ii) The number of students who failed if minimum marks required to pass in the exam is 40.

(iii) If scoring 85 and more marks is considered as grade one, find the number of students who secured grade one in the examination.

• A. i) 57.5, ii) 46, iii) 10
• B. i) 57.5, ii) 46, iii) 16
• C. i) 56.5, ii) 49, iii) 10
• D. i) 57.5, ii) 56, iii) 10

Answer 1

The correct option is B

i) 57.5, ii) 46, iii) 16

$\begin{array}{ccc}Marks& No.ofstudents& c.f.\\ 0-10& 5& 5\\ 10-20& 11& 16\\ 20-30& 10& 26\\ 30-40& 20& 46\\ 40-50& 28& 74\\ 50-60& 37& 111\\ 60-70& 40& 151\\ 70-80& 29& 180\\ 80-90& 14& 194\\ 90-100& 6& 200\end{array}$

i) Median marks will be 57.5 as the x coordinate corresponding to n/2 i.e., 100 is 57.5.

(ii) The number of students who failed is 46, which is the y coordinate corresponding to 40 marks.

(iii) Number of students who secured more than 85 marks (grade one) = Total number of students – 184 = 200 – 184 = 16