SOLUTION: Twelve girls and 8 boys in a class took the same test.
The mean mark for the girls is 65% and the mean mark for the boys is 55%.
(i) Calculate the mean mark of the class overall.
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Question 896073: Twelve girls and 8 boys in a class took the same test.
The mean mark for the girls is 65% and the mean mark for the boys is 55%.
(i) Calculate the mean mark of the class overall.
(ii) Pat said, 'The mode for the boys' marks must be lower than the mode for the girls' marks" Is she correct? Why?
(iii) Kurt said, "A girl must have got the highest mark." I he correct, Why?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
12 girls and 8 boys.
girls average is 65%
boy's average is 55%
overall average is 12*65% + 8*55% with the result being divided by 20.
you get an overall average of 61%.
pat and kurt are both incorrect.
here's an example:
girls scores are:
60
61
62
63
64
65
66
67
68
69
70
65
mode is 65 because 65 occurs 2 times and everything else occurs only one time.
overall average is sum divided by 12 = 780 / 12 = 65
high score is 70
boy's scores are:
90
90
40
41
42
43
44
50
mode is 90 because 90 occurs 2 times and everything else occurs only one time.
overall average equals sum divided by number of occurrences = 440 / 8 = 55.
high score is 90.
(ii) Pat said, 'The mode for the boys' marks must be lower than the mode for the girls' marks" Is she correct? Why?
(iii) Kurt said, "A girl must have got the highest mark." I he correct, Why?
both wrong.
boys mode is higher and boys have the highest score even though the boys mean is lower and the girls had more participants than the boys.
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