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Date May 2010 Marks available 1 Reference code 10M.1.sl.TZ2.5
Level SL only Paper 1 Time zone TZ2
Command term Write down Question number 5 Adapted from N/A

Question

The mean of the ten numbers listed below is 6.8.

8, 5, 5, 10, 8, 4, 9, 7, p, q

Write down an equation in terms of p and q.

[2]
a.

The mode of these ten numbers is five and p is less than q.

Write down the value of p.

[1]
b.i.

The mode of these ten numbers is five and p is less than q.

Write down the value of q.

[1]
b.ii.

Find the median of the ten numbers.

[2]
c.

Markscheme

\(\frac{{8 + 5 + 5 + 10 + 8 + 4 + 9 + 7 + p + q}}{{10}} = 6.8\) or equivalent     (M1)(A1)     (C2)

 

Note: Award (M1) for correct substituted mean formula, (A1) for correct substitution.

 

[2 marks]

a.

p = 5     (A1)(ft)

[1 mark]

 

b.i.

q = 7     (A1)(ft)     (C2)

 

Note: Follow through from their answers to parts (a) and (b) (i).

 

[1 mark]

b.ii.

7     (M1)(A1)(ft)     (C2)

 

Notes: Award (M1) for an attempt to order their numbers.

Follow through from their answers to parts (b)(i) and (ii).

 

[2 marks]

c.

Examiners report

A large number of candidates gained full marks on this question. Many correct variations of the equation were given and the values of p, q and the median could then be found. Some candidates neglected the extra information of p less than q and lost a mark for having these values the wrong way around. Follow through marks could be awarded for the median, if working was shown, with incorrect values of p and q. It was pleasing to see that most candidates realised that a list had to be ordered, before finding the middle value.

a.

A large number of candidates gained full marks on this question. Many correct variations of the equation were given and the values of p, q and the median could then be found. Some candidates neglected the extra information of p less than q and lost a mark for having these values the wrong way around. Follow through marks could be awarded for the median, if working was shown, with incorrect values of p and q. It was pleasing to see that most candidates realised that a list had to be ordered, before finding the middle value.

b.i.

A large number of candidates gained full marks on this question. Many correct variations of the equation were given and the values of p, q and the median could then be found. Some candidates neglected the extra information of p less than q and lost a mark for having these values the wrong way around. Follow through marks could be awarded for the median, if working was shown, with incorrect values of p and q. It was pleasing to see that most candidates realised that a list had to be ordered, before finding the middle value.

b.ii.

A large number of candidates gained full marks on this question. Many correct variations of the equation were given and the values of p, q and the median could then be found. Some candidates neglected the extra information of p less than q and lost a mark for having these values the wrong way around. Follow through marks could be awarded for the median, if working was shown, with incorrect values of p and q. It was pleasing to see that most candidates realised that a list had to be ordered, before finding the middle value.

c.

Syllabus sections

Topic 2 - Descriptive statistics » 2.5 » For simple discrete data: mean; median; mode.
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