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Date May 2015 Marks available 2 Reference code 15M.2.sl.TZ1.3
Level SL only Paper 2 Time zone TZ1
Command term Find Question number 3 Adapted from N/A

Question

The cumulative frequency graph shows the speed, \(s\), in \({\text{km}}\,{{\text{h}}^{ - 1}}\), of \(120\) vehicles passing a hospital gate.

Estimate the minimum possible speed of one of these vehicles passing the hospital gate.

[1]
a.

Find the median speed of the vehicles.

[2]
b.

Write down the \({75^{{\text{th}}}}\) percentile.

[1]
c.

Calculate the interquartile range.

[2]
d.

The speed limit past the hospital gate is \(50{\text{ km}}\,{{\text{h}}^{ - 1}}\).

Find the number of these vehicles that exceed the speed limit.

[2]
e.

The table shows the speeds of these vehicles travelling past the hospital gate.

Find the value of \(p\) and of \(q\).

[2]
f.

The table shows the speeds of these vehicles travelling past the hospital gate.

(i)     Write down the modal class.

(ii)     Write down the mid-interval value for this class.

[2]
g.

The table shows the speeds of these vehicles travelling past the hospital gate.

Use your graphic display calculator to calculate an estimate of

(i)     the mean speed of these vehicles;

(ii)     the standard deviation.

[3]
h.

It is proposed that the speed limit past the hospital gate is reduced to \(40{\text{ km}}\,{{\text{h}}^{ - 1}}\) from the current \(50{\text{ km}}\,{{\text{h}}^{ - 1}}\).

Find the percentage of these vehicles passing the hospital gate that do not exceed the current speed limit but would exceed the new speed limit.

[2]
i.

Markscheme

\(10{\text{ (km}}\,{{\text{h}}^{ - 1}})\)     (A1)

a.

\(36\)     (G2)

b.

\(41.5\)     (G1)

c.

\(41.5 - 32.5\)     (M1)

\( = 9{\text{ (}} \pm {\text{1)}}\)     (A1)(ft)(G2)

 

Notes: Award (M1) for quartiles seen. Follow through from part (c).

d.

\(120 - 110\)     (M1)

\( = 10\)     (A1)(G2)

 

Note: Award (M1) for \(110\) seen.

e.

\(p = 4\;\;\;q = 10\)     (A1)(ft)(A1)(ft)

 

Note: Follow through from part (e).

f.

(i)     \(30 < s \leqslant 40\)     (A1)

 

(ii)     \(35\)     (A1)(ft)

Note: Follow through from part (g)(i).

g.

(i)     \(36.8{\text{ (km}}\,{{\text{h}}^{ - 1}})\;\;\;(36.8333)\)     (G2)(ft)

Notes: Follow through from part (f).

 

(ii)     \(8.85\;\;\;(8.84904 \ldots )\)     (G1)(ft)

Note: Follow through from part (f), irrespective of working seen.

h.

\(\frac{{26}}{{120}} \times 100\)     (M1)

Note: Award (M1) for \(\frac{{26}}{{120}} \times 100\) seen.

 

\( = 21.7{\text{ (}}\% )\;\;\;\left( {21.6666 \ldots ,{\text{ }}21\frac{2}{3},{\text{ }}\frac{{65}}{3}} \right)\)     (A1)(G2)

i.

Examiners report

For the great majority, this was a straightforward and accessible question. There were many, however, who had no appreciation of medians, percentiles and quartiles – all straightforward concepts. Most were able to read from the graph, using correctly the scales; only the weakest misinterpreting these. Calculation of the mean and standard deviation are expected to be completed using the graphic display calculator (GDC) – formulae are no longer required and the covariance will not be given in questions. Many candidates, however, were unable to calculate the mean and standard deviation of a (grouped) frequency distribution, instead treating the data as raw; comments on the G2 forms from schools indicated that some teachers were also unable to do this and advice must be sought.

a.

For the great majority, this was a straightforward and accessible question. There were many, however, who had no appreciation of medians, percentiles and quartiles – all straightforward concepts. Most were able to read from the graph, using correctly the scales; only the weakest misinterpreting these. Calculation of the mean and standard deviation are expected to be completed using the graphic display calculator (GDC) – formulae are no longer required and the covariance will not be given in questions. Many candidates, however, were unable to calculate the mean and standard deviation of a (grouped) frequency distribution, instead treating the data as raw; comments on the G2 forms from schools indicated that some teachers were also unable to do this and advice must be sought.

b.

For the great majority, this was a straightforward and accessible question. There were many, however, who had no appreciation of medians, percentiles and quartiles – all straightforward concepts. Most were able to read from the graph, using correctly the scales; only the weakest misinterpreting these. Calculation of the mean and standard deviation are expected to be completed using the graphic display calculator (GDC) – formulae are no longer required and the covariance will not be given in questions. Many candidates, however, were unable to calculate the mean and standard deviation of a (grouped) frequency distribution, instead treating the data as raw; comments on the G2 forms from schools indicated that some teachers were also unable to do this and advice must be sought.

c.

For the great majority, this was a straightforward and accessible question. There were many, however, who had no appreciation of medians, percentiles and quartiles – all straightforward concepts. Most were able to read from the graph, using correctly the scales; only the weakest misinterpreting these. Calculation of the mean and standard deviation are expected to be completed using the graphic display calculator (GDC) – formulae are no longer required and the covariance will not be given in questions. Many candidates, however, were unable to calculate the mean and standard deviation of a (grouped) frequency distribution, instead treating the data as raw; comments on the G2 forms from schools indicated that some teachers were also unable to do this and advice must be sought.

d.

For the great majority, this was a straightforward and accessible question. There were many, however, who had no appreciation of medians, percentiles and quartiles – all straightforward concepts. Most were able to read from the graph, using correctly the scales; only the weakest misinterpreting these. Calculation of the mean and standard deviation are expected to be completed using the graphic display calculator (GDC) – formulae are no longer required and the covariance will not be given in questions. Many candidates, however, were unable to calculate the mean and standard deviation of a (grouped) frequency distribution, instead treating the data as raw; comments on the G2 forms from schools indicated that some teachers were also unable to do this and advice must be sought.

e.

For the great majority, this was a straightforward and accessible question. There were many, however, who had no appreciation of medians, percentiles and quartiles – all straightforward concepts. Most were able to read from the graph, using correctly the scales; only the weakest misinterpreting these. Calculation of the mean and standard deviation are expected to be completed using the graphic display calculator (GDC) – formulae are no longer required and the covariance will not be given in questions. Many candidates, however, were unable to calculate the mean and standard deviation of a (grouped) frequency distribution, instead treating the data as raw; comments on the G2 forms from schools indicated that some teachers were also unable to do this and advice must be sought.

f.

For the great majority, this was a straightforward and accessible question. There were many, however, who had no appreciation of medians, percentiles and quartiles – all straightforward concepts. Most were able to read from the graph, using correctly the scales; only the weakest misinterpreting these. Calculation of the mean and standard deviation are expected to be completed using the graphic display calculator (GDC) – formulae are no longer required and the covariance will not be given in questions. Many candidates, however, were unable to calculate the mean and standard deviation of a (grouped) frequency distribution, instead treating the data as raw; comments on the G2 forms from schools indicated that some teachers were also unable to do this and advice must be sought.

g.

For the great majority, this was a straightforward and accessible question. There were many, however, who had no appreciation of medians, percentiles and quartiles – all straightforward concepts. Most were able to read from the graph, using correctly the scales; only the weakest misinterpreting these. Calculation of the mean and standard deviation are expected to be completed using the graphic display calculator (GDC) – formulae are no longer required and the covariance will not be given in questions. Many candidates, however, were unable to calculate the mean and standard deviation of a (grouped) frequency distribution, instead treating the data as raw; comments on the G2 forms from schools indicated that some teachers were also unable to do this and advice must be sought.

h.

For the great majority, this was a straightforward and accessible question. There were many, however, who had no appreciation of medians, percentiles and quartiles – all straightforward concepts. Most were able to read from the graph, using correctly the scales; only the weakest misinterpreting these. Calculation of the mean and standard deviation are expected to be completed using the graphic display calculator (GDC) – formulae are no longer required and the covariance will not be given in questions. Many candidates, however, were unable to calculate the mean and standard deviation of a (grouped) frequency distribution, instead treating the data as raw; comments on the G2 forms from schools indicated that some teachers were also unable to do this and advice must be sought.

i.

Syllabus sections

Topic 2 - Descriptive statistics » 2.4 » Cumulative frequency tables for grouped discrete data and for grouped continuous data; cumulative frequency curves, median and quartiles
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