**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.

(a)

**Based on the Table, calculate the estimated mean mark of a student.**

(b)

(b)

**For this part of the question, use graph paper.**

(c)

(c)

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.

**Based on the frequency polygon in**

(d)

(d)

**8(c)**, state the number of students who obtained more than 40 marks.

Answer:

**Table**

*Solution:*

**(a)**

**(b)**

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

**(c)**

**(d)**

Number of students who obtained more than 40 marks

= 10 + 8 + 4

= 22 students