Representing data

The following pictogram shows the number of trees planted by the students of a secondary school over four years. If each symbol represents $5$ trees, answer the following questions:

1. a) How many trees were planted in the year $2021$?
2. b) In which year were exactly $15$ trees planted?
3. c) What is the total number of trees planted over the four years?

The local council of a town wants to raise awareness about recycling. To do so, it has published a pictogram showing the number of recycling bins installed in four different neighbourhoods.

If each ♻️ symbol is equivalent to $12$ bins:

• Neighbourhood A: ♻️♻️♻️♻️

• Neighbourhood B: ♻️♻️♻️

• Neighbourhood C: ♻️♻️♻️♻️♻️

• Neighbourhood D: ♻️♻️

1. a) Construct the frequency table for the number of bins in each neighbourhood.
2. b) What is the total number of bins installed in the town?
3. c) Represent these same data using a bar chart to compare both visual methods.

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

Look at the following bar chart representing the favourite sport of a group of teenagers from a sports club:

Using the graph, answer the following:

1. a) How many people prefer basketball?
2. b) Which sport is the least practised in this group?
3. c) How many people were surveyed in total?

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

The height (in cm) of the $20$ members of a youth basketball club was measured. Being a continuous variable, the data have been grouped into the following intervals:

$[160, 165), [165, 170), [170, 175), [175, 180), [180, 185]$.

The frequencies are: $2, 5, 8, 3, 2$, respectively.

1. a) State the class marks ($x_i$) for each interval.
2. b) Represent the data on a histogram. Explain how this graph differs from a conventional bar chart.
3. c) What is the modal class?

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

To represent the results of a survey about preferred ice cream flavours on a pie chart, we need to calculate the angles for each section. If we know that $10$ out of a total of $40$ people like chocolate, what angle size in degrees ($^\circ$) will the sector corresponding to chocolate have?

A video game company wants to represent the type of console preferred by visitors at a gaming convention in a pie chart. The data are:

• PlayStation: $45\%$

• Nintendo Switch: $30\%$

• Xbox: $15\%$

• PC: $10\%$

1. a) Calculate the degrees corresponding to each circular sector using proportion or the sector angle formula: $\alpha = \frac{360^\circ \cdot n_i}{N}$.
2. b) Draw an approximate pie chart using the calculated angles.

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

Look at the following two graphs showing the change in average temperature in a city during a spring morning. Both represent the same data, but have been drawn with different scales on the vertical axis.

1. a) Explain why Graph B gives the impression of much faster growth than Graph A if the data are identical.
2. b) Which of the two graphs do you think is more objective for informing the public? Reason your answer based on the scale of the vertical axis.

A climate graph (climograph) is a graph that combines a bar chart (rainfall) and a line graph (temperature). Look at the simplified data for a quarter in a city in southern Spain:

• January: $10^\circ C$, $60\text{ mm}$

• February: $12^\circ C$, $45\text{ mm}$

• March: $15^\circ C$, $30\text{ mm}$

1. a) Draw the climate graph, placing the months on the $X$ axis, rainfall on the left $Y$ axis (bars), and temperatures on the right $Y$ axis (line).
2. b) By analysing the graph, what trend do you observe moving from winter to spring?

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