7.4.1 Measures of Dispersion for Grouped Data, SPM Paper (Long Questions)

Question 1:

Solution:
(a) 


Calculation of midpoint for (age 6 – 10) = $\frac{6+10}{2}=8$

(b)(i) 
Modal class = age 16 – 20 (highest frequency)

(b)(ii) 
$\begin{array}{l}\text{mean age =}\frac{3\times 2+8\times 5+13\times 3+18\times 8+23\times 3+28\times 4}{25}\\ \text{=}16.4\end{array}$

(c)

Question 2:
Diagram below shows the marks, obtained by a group of 24 students in a mathematics quiz.

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

(b) State the modal class.

(c) Calculate the estimated marks obtained by a student.


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

(e) Based on the histogram drawn in (d), state the number of students who obtain less than 32 marks in the quiz.

Answer:

Solution:
(a)

(b) Modal class = 27 – 31 (highest frequency)

$\begin{array}{l}\text{(c) }\\ \text{Estimated mean }\\ \text{= }\frac{4\times 24+7\times 29+6\times 34+4\times 39+2\times 44+1\times 49}{24}\\ \text{= }\frac{796}{24}\\ =33.17\text{ marks}\end{array}$


(d)


(e)
Number of students who obtained less than 32 marks
= 4 + 7
= 11