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# Statistics and Probability

## Furthermore

Official Guidance, clarification and syllabus links:

This is designed to cover the key questions that students should ask when they see a data set/analysis.

Dealing with missing data, errors in the recording of data.

Outlier is defined as a data item which is more than 1.5 × interquartile range (IQR) from the nearest quartile.

Awareness that, in context, some outliers are a valid part of the sample but some outlying data items may be an error in the sample.

Link to: box and whisker diagrams (SL4.2) and measures of dispersion (SL4.3).

Simple random, convenience, systematic, quota and stratified sampling methods.

In statistics, the population refers to the entire set of items or individuals under study, while a sample is a subset chosen from this population. A random sample is a sample selected in a way that every member of the population has an equal chance of being included. Data can be categorised as discrete if it can only take specific values (e.g. the number of students in a class) and continuous if it can take any value within a range (e.g. height of a student). The reliability of data sources assesses the consistency and trustworthiness of the data. It's crucial to be aware of bias in sampling, as it can skew results and interpretations. Outliers are data points that significantly differ from the rest of the data and need careful interpretation. Various sampling techniques exist, each with its effectiveness, depending on the situation.

For example, consider a school with $$N$$ students, and we want to calculate the average height. If we measure the height of every student, we are dealing with the population. However, if we measure only a subset (say 30 students randomly chosen), we are dealing with a sample. Suppose the heights of these 30 students are $$x_1, x_2, \dots, x_{30}$$. The sample mean would be:

$$\bar{x} = \frac{x_1 + x_2 + \dots + x_{30}}{30}$$

This sample mean can give us an estimate of the average height of all students in the school, but it may not be the exact population mean.

Sampling methods - aid memoire

• Simple random sampling [GDC skill random integer]
• Systematic sampling [Regular intervals]
• Convenience sampling [Convenient for the experimenter]
• Stratified/Quota sampling [Eg. School survey number from each YG proportional - randomly chosen]

Data Sampling Methods This video covers Data Sampling Methods and is from is from Revision Village

This video on outliers is from Revision Village and is aimed at students taking the IB Maths Standard level course

This Bicen Maths video clip shows everything you need to memorise on Data Collection and Sampling for A Level Statistics.

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