6.7 SPM Practice (Long Questions)

Question 8 (12 marks):
Diagram shows the marks obtained by a group of 36 students in a Mathematics test.

Diagram

(a) Based on the data in Diagram, complete Table in the answer space.

(b) Based on the Table, calculate the estimated mean mark of a student.

(c) For this part of the question, use graph paper.
By using the scale of 2 cm to 5 marks on the horizontal axis and 2 cm to 1 student on the vertical axis, draw a frequency polygon for the data.

(d) Based on the frequency polygon in 8(c), state the number of students who obtained more than 40 marks.

Answer:
Table


Solution:
(a)

(b)
$\begin{array}{l}\text{Estimated mean mark}\\ =\frac{\text{Total }\left[\text{Frequency}\times \text{midpoint}\right]}{\text{Total frequency}}\\ =\frac{\begin{array}{l}2\left(28\right)+5\left(33\right)+7\left(38\right)+10\left(43\right)+\\ 8\left(48\right)+4\left(53\right)\end{array}}{2+5+7+10+8+4}\\ =\frac{1513}{36}\\ =42.03\end{array}$

(c)



(d)
Number of students who obtained more than 40 marks
= 10 + 8 + 4
= 22 students