Higher November 2021 Paper 2 Q7

7 102 boys and 85 girls took a test.

The table shows information about the mean marks.

	Boys	Girls
Number of students	102	85
Mean mark	68.5	72.4

The pass mark for the test was 70

Was the mean mark for all of these students greater than the pass mark?

You must show your working. [3 marks]

Mark scheme

Answer	Mark	Comments
Alternative method 1
\(102 \times 68.5\) or 6987 or \(85 \times 72.4\) or 6154 or 13 141	M1	values may be seen by the table
\(\dfrac{102 \times 68.5 + 85 \times 72.4}{102 + 85}\) or \(\dfrac{13\,141}{187}\) or 70.2(7…) or 70.3	M1dep	oe
70.2(7…) and Yes or 70.3 and Yes	A1
Alternative method 2
\(102 \times 68.5\) or 6987 or \(85 \times 72.4\) or 6154 or 13 141	M1	values may be seen by the table
\((102 + 85) \times 70\) or \(187 \times 70\) or 13 090	M1	oe
13 141 and 13 090 and Yes	A1

Yes may be implied eg \(70.27 \gt 70\)	M1M1A1
M1 may be awarded for correct work, with no or incorrect answer, even if this is seen amongst multiple attempts