Unit 4 sec 1.1

Unit 4 sec 1.1 question questions, types of statistical question

17 November 2015

22:05

You only need to glance at a newspaper, magazine, television or the Internet to see that statistical information is all around you. The key aim of this unit is to present statistical ideas is more than simply facts and techniques - statistical thinking is presented as a helpful way of seeing the world quantitatively.

Mathematical thinking. It can also be viewed in this way and, indeed, many of the remarks and fight statistical in this unit can be equally applied to mathematics in general.

Here are some of the ways in which statistical is unavoidable in our lives

ª    Numbers: Each person operates within a variety of key life roles, such as at work, at home, as a consumer and in the wider community. In each of these environments, you are presented with information, often in the form of the numbers, that must be processed and interpreted you are to be successful. A functioning worker, family member, consumer and citizen.

ª    Graphs and charts: statistical information often takes a visual form. You need to know how to interpret these ‘data pictures’, both in terms of the overall trends and patterns, they suggest, and also by knowing how to pull out and examined some of the relevant details.

Increasingly, almost every subject that you might wish to study has become more quantitative making it ever more important to have a sound grasp of basic statistics.

   Most of this statistical information arises as an attempt to answer questions of various kinds. But they are often end up raising just as many questions as they answer.

    Before rushing into answering any question, it is always a good idea to ask.

Summarising: how can the information be reduced.

Working at a lot of facts and figures does not always provide you with a clear picture of what is going on. To avoid all the world, it is often a good idea to find a way of summarising the information -perhaps by reducing the many figures to just one representative number.

It makes sense to monitor the water quality by taking regular measurements of the quality of the river water. Quite quickly, search and mass of data is generated that it can become difficult to see any underlying patterns. What is needed in some way of reducing many figures into just a few representative ones.

The 2^nd, and equally powerful, way of summarising data is to represent the numbers pictorially using statistical charts or plots -a central theme of unit 11.

Here are some more examples of investigations of the form. How many? Or how much?

¨    How many people die from road accidents each day in the UK?

¨    What is the typical cost of a tube of toothpaste?

¨    How old are the students studying mu123?

These are the sorts of questions were a summary in the form of a simple average can really clarify things.

Comparing: is there a difference

one possible explanation might be that the traffic calming measures have worked. However, there are several problems with this conclusion. 1^st, sample sizes of only 20 too small to be reliable; one speeding car in the 1^st sample may have made all the difference. 2^nd, it is likely that the speeds of different vehicles vary quite a lot, so differences are to be expected. Anyway. 3^rd, the difference between the 2 averages. It was small. And finally, the lower speeds might have been brought about by some other factor, such as a greater density of graphite in the phrase of the experiment. Perhaps because it was school term time.

In general, investigations involving comparing 2 averages will depend on several factors, such as the sizes of the samples on which the averages are based, the degree of variation that one might reasonably expect to see in such values, and whether the size of the observed difference a significantly large to act upon.

·      2 more people, on average, down from road accidents on weekdays or at weekends?

·      How does the cost of brand x toothpaste compare to that of brand y?

·      I students studying mu123. Although are younger than students on an introductory art model?

Seeking a relationship: what sort of relationship is there?

Sometimes a statistical question is not about differences between 2 or more sets of results, but about investigating a possible relationship between quite separate things.

There appears to be a relationship between 2 factors, it is often useful to determine what the relationship is. That is how much does one factor changed relative to the other?

§  Are the numbers of the role deaths in different countries linked to their respective maximum speed limits?

§  How does the cost of tubes of toothpaste depend on their size?

§  What is the connection between the numbers of hours that students work on level III module in mathematics and their final grade?

Classifying statistical investigations

3 types of investigation have been described above

§  Summarising

§  Comparing

§  seeking relationship.

Well summarising investigations are fairly easy to pick out, it can be less easy to distinguish the other 2.

Depending on how the investigation was approached, this could be based either on comparing or unseating a relationship. This will be an investigation based on comparing. However, an alternative experimental design could be to choose a sample of people randomly, measured the running speed and leg length of each person, and see if there is a relationship between these 2 measures.

Exploring questions like those above gives a purpose and direction to statistical learning.