**Attempt this question on graph paper. Marks obtained by 200 students in examination are given below: … , find the minimum marks…**

###### Answers:

(i) Let A be the point on y – axis representing frequency

Here, n (no. of students) = 200 (even)

Median = (n/2)^{th} term

= (200/2)^{th} term

= 100^{th }term

From the graph 100^{th} term = 57.5

(ii) Upper quartile = 3n/4

= (3 × 200^{th})/4 term

= 600/4 = 150th term

From graph 150th term = 72

The upper quartile = 72

(iii) No. of students scoring above 65 marks

⇒ Total No. of students – No. of students scoring ≤ 65 marks

⇒ 200-126

⇒ 74 (approx.)

(iv) From the above diagram, we observe the students from 191 to 200 qualify for merit scholarship.

∴ The students who qualifies for merit scholarship scores more than 91 marks.

∴ The minimum marks required to qualify for merit scholarship

= 92 (approx.)