Use the diagram to estimate the median time.

Use the diagram to estimate the upper quartile and the lower quartile.

Use the diagram to estimate the interquartile range.

Find the number of men who take more than 11 seconds to perform the task.

55 % of the men took less than p seconds to perform the task. Find p.

The times taken for the 2000 men were grouped as shown in the table below.

Write down the value of a.

The times taken for the 2000 men were grouped as shown in the table below.

Write down the value of b.

Use your graphic display calculator to find an estimate of the mean time.

Use your graphic display calculator to find an estimate of the standard deviation of the time.

Everyone who performs the task in less than one standard deviation below the mean will receive a bonus. Pedro takes 9.5 seconds to perform the task.

Does Pedro receive the bonus? Justify your answer.

Unit penalty (UP) applies in this part

(UP)     median = 13 seconds     (A1)

[1 mark]

Unit penalty (UP) applies in this part

(UP)     16 seconds and 10 seconds     (A1)(A1)

Note: Accept 16.1 or 16.2 for the upper quartile value.

IQR = 6 seconds     (A1)(ft)

Note: (ft) from reasonable answers to (ii).

[1 mark]

value seen 650     (A1)

2000 – value = 2000 – 650     (M1)

= 1350     (A1)(G2)

[3 marks]

55 % of 2000 = 1100     (A1)

p = 13.5     (A1)(G2)

[2 marks]

a = 500     (A1)

[1 mark]

b = 150     (A1)

[1 mark]

Unit penalty (UP) applies in this part

(UP)     \( \bar t = 13.25 {\text{ seconds}} \) (13.3 seconds)     (G2)

OR

\(\bar t = \frac{{7.5 \times 500 + 12.5 \times 850 + 17.5 \times {\text{their }}a + 22.5 \times {\text{their }}b}}{{2000}}\)     (M1)

(UP)     \(\bar t = 13.25 {\text{ seconds}}\) (13.3 seconds)     (A1)(ft)

Note: Award (ft) from their a and their b only if working is seen.

[2 marks]

\(\sigma  = 4.41{\text{ seconds}}\)     (G1)

[1 mark]

\(\bar t - \sigma  = 8.84\)     (A1)(ft)

Their \(\bar t - \sigma\) compared to 9.5     (R1)

Pedro does not receive the bonus     (A1)(ft)

Note: Do not award (R0)(A1).

[3 marks]

Most of the students knew the definition of the median, quartiles and inter-quartile range though some confused variables and worked with the frequencies instead. Few could use their calculator to estimate the mean and standard deviation from grouped data. It cannot be said that the calculator was misused but that frequencies and midpoints were ignored when doing the calculations.

Most of the students knew the definition of the median, quartiles and inter-quartile range though some confused variables and worked with the frequencies instead. Few could use their calculator to estimate the mean and standard deviation from grouped data. It cannot be said that the calculator was misused but that frequencies and midpoints were ignored when doing the calculations.

Most of the students knew the definition of the median, quartiles and inter-quartile range though some confused variables and worked with the frequencies instead. Few could use their calculator to estimate the mean and standard deviation from grouped data. It cannot be said that the calculator was misused but that frequencies and midpoints were ignored when doing the calculations.

Most of the students knew the definition of the median, quartiles and inter-quartile range though some confused variables and worked with the frequencies instead. Few could use their calculator to estimate the mean and standard deviation from grouped data. It cannot be said that the calculator was misused but that frequencies and midpoints were ignored when doing the calculations.

Most of the students knew the definition of the median, quartiles and inter-quartile range though some confused variables and worked with the frequencies instead. Few could use their calculator to estimate the mean and standard deviation from grouped data. It cannot be said that the calculator was misused but that frequencies and midpoints were ignored when doing the calculations.

Most of the students knew the definition of the median, quartiles and inter-quartile range though some confused variables and worked with the frequencies instead. Few could use their calculator to estimate the mean and standard deviation from grouped data. It cannot be said that the calculator was misused but that frequencies and midpoints were ignored when doing the calculations.

Most of the students knew the definition of the median, quartiles and inter-quartile range though some confused variables and worked with the frequencies instead. Few could use their calculator to estimate the mean and standard deviation from grouped data. It cannot be said that the calculator was misused but that frequencies and midpoints were ignored when doing the calculations.

Most of the students knew the definition of the median, quartiles and inter-quartile range though some confused variables and worked with the frequencies instead. Few could use their calculator to estimate the mean and standard deviation from grouped data. It cannot be said that the calculator was misused but that frequencies and midpoints were ignored when doing the calculations.

Most of the students knew the definition of the median, quartiles and inter-quartile range though some confused variables and worked with the frequencies instead. Few could use their calculator to estimate the mean and standard deviation from grouped data. It cannot be said that the calculator was misused but that frequencies and midpoints were ignored when doing the calculations.

Most of the students knew the definition of the median, quartiles and inter-quartile range though some confused variables and worked with the frequencies instead. Few could use their calculator to estimate the mean and standard deviation from grouped data. It cannot be said that the calculator was misused but that frequencies and midpoints were ignored when doing the calculations. Part (f) acted as a good discriminator. Follow through marks were awarded in (f) when working was shown.