SPM Mathematics Trial 2024 (Selangor Set 2), Paper 2 (Question 13)


Question 13:
A Selangor state-level STEM quiz competition was conducted to select a representative to the national level. Two participants were involved in the final selection, namely Faris and Danesh. The stem-andleaf plot in Diagram 8 shows the scores obtained by the two participants after several rounds.

(a) Based on the scores obtained by both participants,
(i) state the mode for each participant,  [2 marks]
(ii) calculate the mean score for Faris and Danesh. [2 marks]

(b) Based on the data in Diagram 8, who will be selected for the competition at the national level? Justify your answer. [5 marks]


Solution:
(a)(i)
Mode for Faris = 34
Mode for Danesh = 33 and 41

(a)(ii)
Mean,ˉx=xNMean,¯x=xN
 Mean score for Faris =21+23+24+27+31+34+34+35+42+4310=31.4 Mean score for Faris =21+23+24+27+31+34+34+35+42+4310=31.4
 Mean score for Danesh 17+26+29+33+33+38+41+41+44+4510=34.7 Mean score for Danesh 17+26+29+33+33+38+41+41+44+4510=34.7

(b)
 Standard deviation, σ=x2N(ˉx)2 Standard deviation, σ=x2N(¯x)2
 Standard deviation for Faris =212+232+242+272+312+342+342+352+422+4321031.42=7.255 Standard deviation for Faris =212+232+242+272+312+342+342+352+422+4321031.42=7.255

 Standard deviation for Danesh =172+262+292+332+332+382+412+412+442+4521034.72=8.427 Standard deviation for Danesh =172+262+292+332+332+382+412+412+442+4521034.72=8.427

Faris will be chosen because the score value is more consistent and the standard deviation value is smaller.


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