Question
In a school with 125 girls, each student is tested to see how many sit-up exercises (sit-ups) she can do in one minute. The results are given in the table below. 
(i) Write down the value of p.
(ii) Find the value of q.[3]
Find the median number of sit-ups.[2]
Find the mean number of sit-ups.[2]
Answer/Explanation
Markscheme
(i) \(p = 65\) A1 N1
(ii) for evidence of using sum is 125 (or \(99 – p\) ) (M1)
\(q = 34\) A1 N2
[3 marks]
evidence of median position (M1)
e.g. 63rd student, \(\frac{{125}}{2}\)
median is 17 (sit-ups) A1 N2
[2 marks]
evidence of substituting into \(\frac{{\sum {fx} }}{{125}}\) (M1)
e.g. \(\frac{{15(11) + 16(21) + 17(33) + 18(34) + 19(18) + 20(8)}}{{125}}\) , \(\frac{{2176}}{{125}}\)
mean \(= 17.4\) A1 N2
[2 marks]
Question
The following table gives the examination grades for 120 students.
Find the value of
(i) p ;
(ii) q .[4]
Find the mean grade.[2]
Write down the standard deviation.[1]
Answer/Explanation
Markscheme
(a) (i) evidence of appropriate approach (M1)
e.g. \(9 + 25 + 35\) , \(34 + 35\)
\(p = 69\) A1 N2
(ii) evidence of valid approach (M1)
e.g. \(109 – \) their value of p, \(120 – (9 + 25 + 35 + 11)\)
\(q = 40\) A1 N2
[4 marks]
evidence of appropriate approach (M1)
e.g. substituting into \(\frac{{\sum {fx} }}{n}\), division by 120
mean \(= 3.16\) A1 N2
[2 marks]
1.09 A1 N1
[1 mark]