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Document containing the worksheet   | Complete worksheet   ID: 240101

Description:

In this task, the students are asked to use the most standard statistics parameters:

mean and mean deviation to analyse a statistical distribution. The central parameter (arithmetic mean) can be used to make general comparisons in order to be able to say whether the average value of a variable over a period of time is greater or lower. In any event, this is a rather analysis that should be completed by the mean deviation, as this second parameter indicates whether the distribution is homogeneous or heterogeneous, that is whether the values are together, in relation to the mean, or separate. It is an important datum in the case of climatology as climates with equal arithmetic means can be quite different in the sense that one of them may be more extreme (greater mean deviation) than the other.

Competences:

Using the central parameters to analyse and interpret a set of data.

Difficulty (1: low - 3: high):

2   Task type: Experience   Estimated time: 30 min.

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Document containing the worksheet   | Complete worksheet   ID: 240102

Description:

In this task, the students are asked to use the most standard statistics parameters:

mean and mean deviation to analyse a statistical distribution. The central parameter (arithmetic mean) can be used to make general comparisons in order to be able to say whether the average value of a variable over a period of time is greater or lower. In any event, this is a rather analysis that should be completed by the mean deviation, as this second parameter indicates whether the distribution is homogeneous or heterogeneous, that is whether the values are together, in relation to the mean, or separate. It is an important datum in the case of climatology as climates with equal arithmetic means can be quite different in the sense that one of them may be more extreme (greater mean deviation) than the other. In the second part of this task, the students are asked to interrelate the means and mean deviations obtained in different provinces; they are therefore asked to interpret the data to be able to compare the climates of both territories appropriately.

Competences:

Calculating and using deviation parameters to analyse and interpret a set of data.
Using the central parameters to analyse and interpret a set of data.

Difficulty (1: low - 3: high):

2   Task type: Experience   Estimated time: 30 min.

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Document containing the worksheet   | Complete worksheet   ID: 240103

Description:

This is both a new and interesting task because this is the start of the process

to learn one of the most interesting and complex Statistics concepts studied in these courses. A table is provided in this task with data on the climatology of the Guipuzkoa observatories: the tables contains the data about the height at which they are located (m), the amount of water collected or rainfall (l/m2) and the annual mean temperature. Two graphs are also provided: the first relates the height and the temperature and the second the height and the rainfall. In the graph that relates height with temperature, you can see that the data are quite grouped together around an imaginary line that crosses them; the points are more disperse in the height and rainfall relation graph and their shape are more similar to a “cloud” than a line. Therefore, the intuitive ideas of line and cloud are the base to relate the points to the correlation concept. The more aligned the points are, the greater the correlation is between the distribution values, the less aligned and more cloud like, the lower the correlation is.

Using these ideas, it is easy to affirm that the correlation is greater in the case of the relationship between the height and the temperature than between the height and the precipitation.

In the case of the high correlation, this is negative as the temperature lowers as the height increases, as can be seen in the graphs.

The second part of this task consists of a series of questions that aim to guide the reflection process about this concept and, thus, be able to reach specific conclusions.

Competences:

Identifying the correlation concept between variable intuitively by interpreting the points diagram that join the value of the distributions to be analysed.

Difficulty (1: low - 3: high):

2   Task type: Experience   Estimated time: 30 min.

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Document containing the worksheet   | Complete worksheet   ID: 240104

Description:

This task continues to work on the intuitive aspects of the correlation concept

to which an intuitive approach to the concept is added and the regression line drawn.

A table and two graphs are provided. The table contains the data from the observatories where the height at which they are located and the mean maximum and minimum temperatures are indicated. The graphs represent the value pairs that correspond to: a) mean maximum temperature and height and b) mean minimum temperature and height. They are two interesting cases because while the correlation seems high in one of them (height - mean maximum temperature); the points are much more disperse in the other (height - mean minimum tempeature) which allows the meaning of this concept to be seen. This is precisely what the students must know how to conclude in order to be able to complete the titles of the graphs. The OY axis data may help them with this task, and in any event, they should be made to reflect about the correlation existing in both cases.

One those points are represented on the diagrams, the ruler can be placed on them and the regression lines drawn in. What the students have to try to achieve is that the number of points on either side of the line is as similar as possible and that the distance from them to the line is as small as possible. The best thing is to draw them with a pencil to be able to erase them over and over again until they are correct. This line predicts the related value pairs approximately and the approximation is better the higher the correlation of the variables.

Competences:

Drawing, approximately, the regression line of a set of data.
Identifying the correlation concept between variable intuitively by interpreting the points diagram that join the value of the distributions to be analysed.

Difficulty (1: low - 3: high):

2   Task type: Research   Estimated time: 30 min.

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Document containing the worksheet   | Complete worksheet   ID: 240105

Description:

This task involves a table which contains different meteorological data. We

have chosen one of the them to study possible correlations: the height of the weather station; and we wish to study the relation existing between this value and the other three chosen: The number of days of ice, the mean daily humidity and the speed of the maximum wind gust.

Points diagrams are there built for each of those three cases:
a) height of the weather station, number of days of ice;
b) height of the weather station, mean daily humidity;
c) height of the weather station, speed of the maximum wind gust.
Once these diagrams are built, the set of points can be analysed and the students can attempt to reach some conclusions about them.

They are three different cases: The correlation is weak in the first one, it is quite strong in the second and it is intermediary in the third one. They are thus interesting cases as they mean that different situations can be compared and some conclusions can be reached very intuitively. In any case, the more or less intense correlation is positive.

Competences:

Using the concept of correlation between variables to analyse the relations between data distribution pairs.

Difficulty (1: low - 3: high):

2   Task type: Research   Estimated time: 40 min.

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Document containing the worksheet   | Complete worksheet   ID: 240106

Description:

This task involves a table which contains different meteorological data. We

have chosen one of them to study possible correlations: the height of the weather station; and we wish to study the relation existing between this value and the other three chosen: The number of days of ice, the mean daily humidity and the speed of the maximum wind gust.

Points diagrams are there built for each of those three cases:
a) height of the weather station, number of days of ice;
b) height of the weather station, mean daily humidity;
c) height of the weather station, speed of the maximum wind gust.
Once these diagrams are built, the set of points can be analysed and the students can attempt to reach some conclusions about them.

They are three different cases: The correlation is weak in the first one, it is quite strong in the second and it is intermediary in the third one. They are thus interesting cases as they mean that different situations can be compared and some conclusions can be reached very intuitively. In any case, the more or less intense correlation is positive.

Competences:

Using and calculating the concept of correlation between variables and to analyse the relations between data distribution pairs.

Difficulty (1: low - 3: high):

2   Task type: Experience + Research   Estimated time: 40 min.

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Document containing the worksheet   | Complete worksheet   ID: 240107

Description:

This task aims to study the relation existing between the length of a river

and its average flow, on the one hand, and between that length and the extension of its basin, on the other hand.
The relevant points clouds are drawn using the table data; as can be seen, both clouds are different. In the first of the cases, the cloud is less grouped than in the second and several conclusions can be put forward from this observation. The questions from the second part of this task can be used to reach conclusions and try to justify them. Drawing the regression line can help us to reach more conclusions. The regression line equation can be used to estimate results.

Competences:

Using the central parameters to analyse and interpret a set of data.
Using the concept of correlation between variables to analyse the relations between data distribution pairs.

Difficulty (1: low - 3: high):

2   Task type: Experience   Estimated time: 20 min.

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Document containing the worksheet   | Complete worksheet   ID: 240108

Description:

In this task we try to relate the statistical values and the probability of

something happening. The underlying idea is that the probability increases if the value of a parameter is higher. Thus if the number of rainy days on average is higher, the probability that there is a rainy day when chosen at random is greater. The mean values are not use to make this prediction as they indicate the average between the different places but they do not provide information on the specific situation of each of them.

The points cloud that relates them are shown in the second part of this tasks and the aim is for the students to work on the correlation between both variables and, subsequently, they reach and justify the conclusions from this analysis. The possible prediction depends on the existing correlation level between both variables.

Competences:

Calculating and using deviation parameters to analyse and interpret a set of data.
Reading, carefully, and interpreting, critically, the statistical information contained in tables, graphs, diagrams or texts, and distinguishing between relative and absolute data (percentages, rates).
Using the central parameters to analyse and interpret a set of data.
Using the concept of correlation between variables to analyse the relations between data distribution pairs.

Difficulty (1: low - 3: high):

2   Task type: Experience   Estimated time: 50 min.

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Document containing the worksheet   | Complete worksheet   ID: 240109

Description:

In this task, the students carry out some small research in order to study the

relations between the chosen variables. The interpretation of the points cloud can lead to an initial intuitive approach to the correlation existing between the variables, the correlation coefficient calculation must help them to refine this first approach further and to find better founded conclusions. As we always say, the degree of autonomy with which the students tackle those tasks is fundamental in order to develop the competences associated to those tasks.

Competences:

Using the concept of correlation between variables to analyse the relations between data distribution pairs.

Difficulty (1: low - 3: high):

2   Task type: Research   Estimated time: 40 min.

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Document containing the worksheet   | Complete worksheet   ID: 240110

Description:

This task provides information about the meaning of the correlation between

variables and the regression line that is used to carry out estimates using them.

In this task, the students are given a text “to study”, in the same way as in the summarising activities. Studying means using some learning strategies or techniques in order to process the information. It is proposed to use the following techniques for this task:
a) Read the text and any words or terms that are not understood.
b) Identify the concepts that are explained and defined; in this case they are: median and quartiles.
c) Underline the definitions.
d) Building a glossary with the definitions.
e) Memorising the definitions entered in the glossary.

A series of exercises are provided in this task to check to which point the information supplied in the first part of the task has been understood. They are, therefore, exercises to apply what has been learnt.

Competences:

Interpreting, summarising and memorising statistical data.

Difficulty (1: low - 3: high):

2   Task type: Synthesis   Estimated time: 30 min.

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Document containing the worksheet   | Complete worksheet   ID: 240111

Description:

A series of exercises are provided in this task to check to which point the

information supplied in the educational unit has been understood.

Competences:

Identifying, analysing and solving problems.

Difficulty (1: low - 3: high):

2   Task type: Test   Estimated time: 40 min.