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+43210−31.42=7.255 Standard deviation for Faris =√212+232+242+272+312+342+342+352+422+43210−31.42=7.255
Standard deviation for Danesh =√172+262+292+332+332+382+412+412+442+45210−34.72=8.427 Standard deviation for Danesh =√172+262+292+332+332+382+412+412+442+45210−34.72=8.427
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+43210−31.42=7.255 Standard deviation for Faris =√212+232+242+272+312+342+342+352+422+43210−31.42=7.255
Standard deviation for Danesh =√172+262+292+332+332+382+412+412+442+45210−34.72=8.427 Standard deviation for Danesh =√172+262+292+332+332+382+412+412+442+45210−34.72=8.427
Faris will be chosen because the score value is more consistent and the standard deviation value is smaller.