SPM Additional Mathematics 2019, Paper 2 (Question 5)

Question 5:
Table 1 shows the deviation from the mean mark scored by Nora in a monthly test. The deviation from the mean mark for Sejarah has been left out.

Table 1

It is given that her mean mark for all the 9 subjects is 60.
Find
(a) the median mark, [4 marks]
(b) the standard deviation. [3 marks]

Solution:
(a)

\begin{array}{l} Mean mark = 60 \\ \frac{450 + m}{9} = 60 \\ 450 + m = 540 \\ m = 90 \end{array}

$\begin{array}{l} Mean mark = 60 \\ \frac{450 + m}{9} = 60 \\ 450 + m = 540 \\ m = 90 \end{array}$

Mark for Sejarah = 90
38, 40, 41, 54, 62, 62, 70, 83, 90
Median mark = 62

(b)

\begin{array}{l} Standard deviation = \sqrt{\frac{2818}{9}} \\ = 17.695 \end{array}

$\begin{array}{l} Standard deviation = \sqrt{\frac{2818}{9}} \\ = 17.695 \end{array}$

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