Exercises: Observation and data analysis

The temperature of a glass of hot water cooling on a table is measured: at 0 min it reads $60\ ^\circ\text{C}$, at 5 min $52\ ^\circ\text{C}$, at 10 min $45\ ^\circ\text{C}$, at 15 min $40\ ^\circ\text{C}$, and at 20 min $36\ ^\circ\text{C}$. What was the temperature at 10 minutes? In which time interval did the temperature drop the fastest?

You want to represent three sets of data: (a) how classroom temperature changes throughout the day, (b) the percentage of students choosing each sport, and (c) the number of different species observed in each area of the playground. State which type of graph (line graph, circle graph, or bar graph) you would choose in each case and justify your choice.

The graph shows the height reached by some plants depending on the hours of light they receive each day. Describe the relationship between both variables and, using the grid lines to help you, estimate the approximate height of a plant receiving 6 hours of light per day.

A bean plant, which sprouts at the start of the first week with a height of 0 cm, is 2 cm tall at the end of the first week, 6 cm at the end of the second, 11 cm at the end of the third, and 17 cm at the end of the fourth. Calculate how much it has grown in total and its mean weekly growth, and determine whether it has grown at the same rate every week.

It is observed that the months with the highest ice cream sales are also the months with the most bathers on the beach. Does that mean eating ice cream causes people to go to the beach? Explain the difference between correlation and causation using this example.

Two groups measure the length of the same leaf three times. Group A gets $8.1\ \text{cm}$, $8.3\ \text{cm}$, and $8.2\ \text{cm}$; Group B gets $7.5\ \text{cm}$, $9.0\ \text{cm}$, and $8.1\ \text{cm}$. Calculate the mean for each group and determine which of the two measured with greater precision.

When measuring the time it takes for a leaf to fall from $2\ \text{m}$, the following values in seconds are obtained: 3.1, 2.9, 3.0, 7.8, 3.2. One of them is clearly anomalous. Identify it, suggest a possible cause for this error, and decide, with reasoning, what to do with this data point when calculating the mean.

You are going to investigate whether soil type (sand, clay, or garden soil) affects the growth of lentil plants over 15 days. Design the data table you would use to collect the results: state what columns and rows it would have and what units you would use.

A study finds that students who spend more hours in the library get better marks, and a newspaper headline reads: "The library boosts marks". Give at least two alternative explanations for this correlation and explain what type of experiment would be needed to state that a cause-and-effect relationship exists.