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Date May 2008 Marks available 5 Reference code 08M.1.sl.TZ2.1
Level SL only Paper 1 Time zone TZ2
Command term Find Question number 1 Adapted from N/A

Question

A box contains 100 cards. Each card has a number between one and six written on it. The following table shows the frequencies for each number.


Calculate the value of k.

[2]
a.

Find

(i)     the median;

(ii)    the interquartile range.

[5]
b(i) and (ii).

Markscheme

evidence of using \(\sum {{f_i} = 100} \)     (M1)

\(k = 4\)     A1     N2

[2 marks]

a.

(i) evidence of median position     (M1)

e.g. 50th item, \(26 + 10 + 20 = 56\)

\({\text{median}} = 3\)     A1     N2

(ii) \({Q_1} = 1\) and \({Q_3} = 5\)     (A1)(A1)

\({\text{interquartile range}} = 4\) (accept 1 to 5 or \(5 - 1\) , etc.)     A1     N3

[5 marks]

 

b(i) and (ii).

Examiners report

Frequencies and median seemed well understood, but quartiles and inter-quartile range less so.

a.

Frequencies and median seemed well-understood, but quartiles and interquartile range less so. A few students, probably based on past papers, drew cumulative frequency diagrams, generating slightly different answers for median and quartiles.

b(i) and (ii).

Syllabus sections

Topic 5 - Statistics and probability » 5.2 » Central tendency: mean, median, mode.
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