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Date May 2014 Marks available 4 Reference code 14M.2.sl.TZ2.3
Level SL only Paper 2 Time zone TZ2
Command term Estimate Question number 3 Adapted from N/A

Question

A survey was conducted to determine the length of time, t, in minutes, people took to drink their coffee in a café. The information is shown in the following grouped frequency table.


Write down the total number of people who were surveyed.

[1]
a.

Write down the mid-interval value for the 10<t15 group.

[1]
b.

Find an estimate of the mean time people took to drink their coffee.

[2]
c.

The information above has been rewritten as a cumulative frequency table.


Write down the value of a and the value of b.

[2]
d.

This information is shown in the following cumulative frequency graph.



For the people who were surveyed, use the graph to estimate

(i)     the time taken for the first 40 people to drink their coffee;

(ii)     the number of people who take less than 8 minutes to drink their coffee;

(iii)     the number of people who take more than 23 minutes to drink their coffee.

[4]
e.

Markscheme

60     (A1)

[1 mark]

a.

12.5     (A1)

[1 mark]

b.

3×2.5+5×7.5++10×27.560     (M1)

 

Note: Award (M1) for an attempt to substitute their mid-interval values (consistent with their answer to part (b)) into the formula for the mean.

     Award (M1) where a table is constructed with their (consistent) mid-interval values listed along with the frequencies.

 

=107560 (21512, 17.9, 17.9166)     (A1)(ft)(G2)

 

Note: Follow through from their answer to part (b).

 

[2 marks]

c.

a=34, b=60     (A1)(A1)

[2 marks]

d.

(i)     21.25 minutes     (A1)

 

Note: Accept 21.25.

     Accept any answer between 21 and 21.5.

     (Accept 21.5, but do not accept 21.)

 

(ii)     5     (A1)

 

Note: Accept <6. Do not accept 6.

     Answer must be an integer.

 

(iii)     6045     (M1)

=15     (A1)(G2)

 

Notes: Award (M1) for subtraction from 60. Accept 15±1.

     Answer must be an integer.

 

[4 marks]

e.

Examiners report

[N/A]
a.
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b.
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c.
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d.
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e.

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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