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Data Trends Analysis

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Data Trends Analysis

A local council is reviewing active travel and weather patterns. Analyse the supplied data, describe trends with evidence, and make cautious inferences. For written answers, distinguish association from causation. Round calculations to 2 decimal places where needed.

Daily temperature and cycle counts

A sensor recorded the afternoon temperature and the number of cyclists passing a point on six days.

Day

Temperature (°C)

Cyclists

Mon

Tue

Wed

Thu

Fri

Sat

1.Describe the association between temperature and cyclist count. Refer to direction, form, strength, and at least two data values as evidence.

2.Which statement is best supported by these observations?

Warmer afternoons caused every increase in cycling.
The observed cyclist count tended to be higher on warmer afternoons.
Temperature and cyclist count have no association.
The data prove that all people cycle more in summer.

3.The council wants to estimate the cyclist count at 18°C using the overall pattern. Give a reasonable estimate and explain why it is an interpolation rather than an extrapolation.

Monthly rainfall: find the pattern

Monthly rainfall (mm) was recorded at a monitoring site near the coast. Use the table to look for seasonality and unusual values.

Month

Jan

Feb

Mar

Rain (mm)

Month

Apr

May

Jun

Rain (mm)

104

139

156

Month

Jul

Aug

Sep

Rain (mm)

171

148

112

Month

Oct

Nov

Dec

Rain (mm)

4.Identify the broad seasonal pattern in this rainfall series. Support your description with the wettest and driest months and their values.

5.Calculate the range of monthly rainfall. Show the subtraction you use.

6.Give one reason why one year of monthly data is not enough to claim that this seasonal pattern happens every year.

Compare distributions and check claims

Two groups of students recorded their one-way travel time to a community sports centre (minutes).

Group

Minimum

Group

Median

Bus users

Walkers

Group

Maximum

IQR

Bus users

Walkers

7.Compare the typical travel times for bus users and walkers. Use the medians and interpret the difference in context.

8.Verify the interquartile range (IQR) for each group, then state which group has the greater spread in the middle 50% of travel times.

9.A report says, “Because the bus group’s maximum is 51 minutes, most bus users take about 51 minutes.” Explain why this conclusion is not supported by the summary.

10.The council wants to know whether warmer weather increases cycling. Name one additional variable to collect and explain how it could help assess this claim.