Thinking Skills: Critical Thinking and Problem Solving

5.4 Data analysis and inference 229

b Which teams can still qualify for the

next stages and what results of the final

two matches will be needed to send

each possible pair of teams through?

(Note: in the event of a draw on points

between two teams, the results of the

match between those two teams will

decide who goes through; if this was

a draw, the difference between goals

scored and goals conceded decides

and, if this is equal, the team with the

most goals scored will go through. If all

else fails, qualification will be decided

by the drawing of lots.)

3 The exercise below is open-ended, in

that no specific questions are asked.

This is quite typical of real-world problem-

solving in relation to scientific work. The

experimenter should come to the results

with an open mind and squeeze as much

information from them as possible (without

claiming too much where the results are

not entirely clear).

An experiment was carried out to study

the growth of doba-berries using a range

of amounts of water and fertiliser. 30

beds were laid out, each with an area of

1 square metre. They were each watered

daily with amounts of water from 5 to

30 litres. At the start of the experiment

amounts of fertiliser from 0 g to 25 g were

applied to each plot. When the crop was

ripe, the yield from each square metre was

measured. The results are shown in the

following table. The results for a fertiliser

application of 10 g are missing because of

a problem with the beds.

Analyse this data and draw conclusions

on the effect of water and fertiliser on

the crop. Also consider how the two

factors may interact with each other. A full

statistical analysis is not required; the

conclusions may be drawn by averaging

and graphing the data in various ways.

to a sharp rise in prices, reaching levels

second only to those seen in 2008.

Of greater long-term concern,

proven oil reserves worldwide grew

only 0.5% in 2010, to 1368 billion

barrels... So, consumption growth of

3.1% was six times the growth of

reserve identification, spelling

long-term trouble for prices.

Given that reserves are finite and world

energy consumption is rising, what would

be the implications of higher prices and

less use of fossil fuels on world energy

reserves and consumption?

2 In the group stages of a European football

tournament, teams were in groups of four

in which each team played all the others,

making six games in total. The top two

teams in each group after this stage went

through to the quarter-finals. Teams were

awarded three points for a win, one for a

draw and none for losing. After four matches

in Group 1, the situation was as follows.

(Some data is missing from the table.)

Team Played Points W D L Goals

for

Goals

against

Greece 2 4 3 2

Spain 2 4 2 1

Portugal 2 3 3 2

Russia 2 0 0 3

The remaining two games are Spain vs

Portugal and Greece vs Russia.

a Can you reconstruct the missing data

(games won, drawn and lost for each

team)? How much further can this be

taken: can the results of individual

games be established; can the scores

be deduced?