Find the value of \(p\) .

Find

  (i)     the mean;

  (ii)     the variance.

valid approach     (M1)

eg   \(35 - 26\) , \(26 + p = 36\)

\(p = 9\)     A1     N2

[2 marks]

(i)     mean \( = 26.7\)     A2     N2

(ii)     recognizing that variance is (sd)²     (M1)

eg   \(11.021{ \ldots ^2}\) , \(\sigma  = \sqrt {{\mathop{\rm var}} } \) , \(11.158{ \ldots ^2}\)

\({\sigma ^2} = 121\)     A1     N2

[4 marks]

Candidates had little problem determining a missing frequency from a cumulative frequency table.

In part (b), few used the GDC to their advantage to correctly find the mean and variance. There were numerous unsuccessful attempts at using the formulae for mean and variance, most resulting in algebraic errors along the way. Candidates recognized the concept of variance but were often unable to determine what value should be squared.