 # SPM Mathematics Trial 2021 (Selangor), Paper 2 (Question 13)

Question 13:
Data in Table 1 shows the height, in cm, of a group of 10 volleyball players.

 142 168 162 154 172 162 157 158 169 181
Table 1

(a)
Determine
(i) the first quartile
(ii) median
(iii) the third quartile
(iv) the interquartile range
[4 marks]

(b) Table 2.1 shows the number of words typed by a group of participants in a Shorthand and Secretarial Workshop within the duration of 5 minutes.

 Number of words Frequency 121 – 125 6 126 – 130 9 131 – 135 13 136 – 140 18 141 – 145 14 146 – 150 10
Table 2.1

Complete Table 2.2 in the answer space 13(b).
Calculate standard deviation of the data.
[6 marks]

(b)
 f Midpoint fx x2 fx2 6 123 9 128 13 133 18 138 14 143 10 148 Σ f = 70 Σ fx = Σ x2 = Σ fx2 =

Solution:

142, 154, 157 (Q1), 158, 162, | 162, 168, 169 (Q3), 172, 183

(a)(i) the first quartile, Q1 = 157

(a)(ii) $\text{median}=\frac{162+162}{2}=162$

(a)(iii) the third quartile, Q3 = 169

(a)(iv) the interquartile range = Q– Q= 169 – 157 = 12

(b)
 f Midpoint fx x2 fx2 6 123 738 15 129 90 774 9 128 1 152 16 384 147 456 13 133 1 729 17 689 229 957 18 138 2 484 19 044 342 792 14 143 2 002 20 449 286 286 10 148 1 480 21 904 219 040 Σ f = 70 Σ fx = 9 585 Σ x2 = 110 599 Σ fx2 = 1 316 305