3.8 Hypotheses, reasons, explanations and inference 107
So A and C are the explanations for the shape
of the curve.
The activity below is firmly in the
Cambridge Thinking Skills syllabus category of
‘suggesting hypotheses for variations’. You are
given a scenario incorporating numerical data,
and asked which, of a number of possible
situations, could explain the nature of the data.
Nikul runs exercise classes at his local gym,
and gets there each day by train and bus.
Classes start at different times each day, but
always either on the hour or at half past the
hour. He always gets to the railway station
45 minutes before he is due to start teaching
and the train journey takes 20 minutes, after
which he takes a bus to the gym, which takes
10 minutes. Trains leave every 20 minutes,
starting on the hour. Some days Nikul finds
that he gets to work 5 minutes early. On all
the other days he finds that he gets there
5 minutes late.
Which one of the following could explain
the times that Nikul arrives at the gym?
A The buses leave at 5 and 35 past
each hour.
B The buses leave at 15 and 45 past
each hour.
C The buses leave at 25 and 55 past
each hour.
D The buses leave at 5, 25 and 45 past
each hour.
E The buses leave at 15, 35 and 55 past
each hour.Activity
Commentary
Nikul arrives at the station at either 15 or 45
past the hour. Therefore, he takes the train
either on the hour or at 20 past the hour. He
gets to the bus stop at 20 or 40 past the hour.
Buses at 5, 25 and 45 past the hour would
therefore fit the requirements:
• He would get the bus at 25 past the hour
if he arrived at 20 past. This would mean
that he arrived at work 5 minutes late.
• He would get the bus at 45 past the hour
if he arrived at 40 past. This would mean
that he arrived at work 5 minutes early.
• He would never use the bus at 5 past the
hour, so it doesn’t matter that this one
doesn’t fit the arrival times.The correct answer is D. It is also illustrative to
see why the wrong answers do not work:
A Buses at 5 and 35 past the hour would
always get Nikul to work on a quarter hour
which could not be 5 minutes early
or late.
B Buses at 15 and 45 past the hour would
mean that Nikul was always 5 minutes
early.
C Buses at 25 and 55 past the hour would
mean that Nikul was always 5 minutes late.
E Because Nikul arrives on the train at 20 or
40 past the hour, he would be getting the
35 or 55 past the hour bus. The bus at 35
past the hour would get Nikul to work at
15 or 45 past the hour which is neither 5
minutes early nor 5 minutes late.
Longer questions at A Level can involve
analysing quite complex data and determining
what conclusions may be drawn from it. The
activity below is of this type. It looks at
identifying reasons for variations in data.