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, pie chart, or bar chart) 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.

Explain the difference between qualitative data and quantitative data, and classify these observations from the playground: "the flowers are yellow", "there are 14 bees", "the leaves are $5\ \text{cm}$ long", and "the air smells of wet grass".

You have counted the pigeons seen in the playground over five days: 12, 9, 15, 11, and 14. Draw a properly made data table, with a title and column headings, to record those values.

You can do it on paper and send a photo with your answer.

A table reads: "the school sports court measures 100". Explain what information is missing for the data to be complete and why units are essential in a table of scientific data.

In a bar chart about animals seen in the park, the bars show: sparrows 8, pigeons 5, blackbirds 2, and squirrels 1. Which animal was observed most often? How many animals were counted in total? What title would you give the chart?

To study how a plant grows we measure its height every week. State which quantity we are measuring, which instrument you would measure it with, and in which unit you would express the data.

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.

The maximum temperatures one week were 20, 22, 23, 25, 24, 26, and 21 degrees Celsius. Calculate the mean temperature for the week and point out which two days were furthest from that mean.

You are going to plot on a line graph how the depth of a puddle changes over ten days of drought. Explain which variable you will place on each axis, which units you will use, and why time is almost always plotted on the horizontal axis.

Five classmates measure their resting heart rates and get 72, 80, 68, 76, and 74 beats per minute; after running for two minutes they get 108, 116, 102, 110, and 104. Calculate the mean in each situation and write a two-line conclusion.

A bar chart about the class's favourite fruits has no title, no axis labels, and it is not known how many people were asked. Explain what problems this chart has when it comes to being interpreted and which three things you would add.

To find out the favourite sport of the school's students, a group decides to ask only the members of the football team. Explain why this sample does not represent the whole school and describe how you would choose the sample so that the result was more reliable.

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.

You suspect there are more invertebrate species in the sunny area of the playground than in the shady area. Design the fieldwork: how you will make the counts so they are comparable (same time, same hours, same effort), which table you will use to collect the data, and which type of graph you would choose to compare both areas. State also how you will respect the animals.

Two bar charts show the same data on visits to two libraries, but in one the vertical axis starts at 0 and in the other it starts at 950 visits, so the difference between the bars looks enormous. Explain which trick is being used, why it can mislead the reader, and what an honest chart should look like.

Mini-project: measure the classroom temperature three times a day (first thing in the morning, at midday, and at the end of the school day) for a week. Before starting, predict the shape the line graph will have; then organise the data into a table, draw the graph, and comment on two factors that may have altered the values (the heating, open windows, the number of people).

You can do it on paper and send a photo with your answer.

The marks of two groups of five students are: group A, 2, 5, 6, 7, and 10; group B, 6, 6, 6, 6, and 6. Calculate the mean of each group and explain why, although the means are the same, the two groups are not alike; explain what information is lost when only the mean is given.

In a germination experiment, out of 10 lentils soaked in water, 8 germinated in three days, whereas out of 10 unsoaked lentils, 5 germinated. Organise the data into a table, calculate the germination percentage of each condition, and write a three-line conclusion stating whether soaking seems to help and what you would do to confirm it.