Statistics is how we collect, analyse and interpret data. You can work with data in a variety of ways: visually with graphs, calculating averages, or exploring probability. Statistics has relevance in our day-to-day, such as understanding the news and making predictions using data trends.
This guide is a brief overview of the various topics in statistics. This includes mean, median and mode, data representation and sampling methods. If you need extra support, TeachTutti has a list of GCSE Maths tutors who can help you revise this and other topics in the GCSE Maths curriculum.
What is statistics?
Statistics is how we collect, analyse, interpret and present data. There are various topics in GCSE Maths: understanding different types of data, calculating averages and using charts and graphs. Ultimately, the target is to present and understand numbers and trends, which is important in everyday situations e.g. comparing prices or understanding probabilities in games.
For example, one topic in statistics is types of data. This includes qualitative data - called descriptive - and quantitative data - called numerical. You are expected to know if the data given is discrete, with specific values, or continuous and have any value within a range. This and other topics are the foundation of statistical analysis, giving us the tools to choose the correct method to analyse data sets.
1
What data type would be the number of students in a classroom?
Key concepts in GCSE Statistics
One of the key concepts in statistics is measures of central tendency, which is how we summarise data sets with a single value. These measures are mean, median and mode. We get the overall average using the mean by adding all values and dividing by the number of items. The middle value is found using the median when the data is ordered. This is a better measure when extreme values of outliers are present, which skews the mean value. The mode is value that occurs the most frequently, which is helpful for categorical data.
Measures of dispersion is the spread of data. The simplest measure is the range, which shows the difference between the highest and lowest values. This can be affected by outliers, unlikely the interquartile range (IQR), which is more sophisticated and looks at the middle 50% of the data to see where most values lie.
We use data distribution to show how data points are spread across different values. Data is spread evenly in the centre in symmetric distributions. This is opposed to skewed distributions, where data tends to cluster to one side. Data distribution is useful for spotting patterns and interpreting results accurately.
It's important to understand the different types of data. We use qualitative data for descriptions and characteristics, such as colour or type. This is normally presented in word format. Quantitative data involves numbers and measurements. It can be broken down into discrete data (countable items e.g. the number of students) and continuous data (measurable quantities e.g. temperature).
2
Which measure of central tendency do extreme values (outliers) affect?
Data representation
Statistics is often simplified by presenting the data visually with bar charts, histograms, pie charts and line graphs. Each graph type has a specific purpose so be careful with your choice. For example, we can compare discrete categories using bar charts, while histograms show frequency distributions with continuous data. Follow the link for Atlassian's explanation of a histogram.
It's crucial to interpret these charts accurately as well as draw them correctly. It won't come as a surprise that conclusions will be incorrect if the data is misread. Learning how you can efficiently spot trends, compare data sets and spot outliers.
For instance, it's a good idea to use pie charts to show proportions. However, it's less helpful when there are too many categories, unlike a histogram, which can clearly show patterns and ranges in large data sets.
3
What graph would you use to show the distribution of a continuous data set?
Sampling methods
Sampling is when you draw conclusions on an entire group from a chosen subset of the population. There are different sampling methods in GCSE Maths, including random, systematic and stratified sampling. Each method has its strengths and weaknesses that you need to weigh up when choosing the best method for your problem:
- Random sampling - Every member of the population has an equal chance of being selected. This removes the possibility of bias.
- Systematic sampling - Every nth individual is selected. This is straightforward but may unintentionally create a pattern that doesn't accurately represent the population.
- Stratified sampling - The population is divided into subgroups (strata) and sampled proportionally from each group. The important subgroups are represented clearly.
The right sampling method will remove bias and avoid incorrect conclusions. Think about the purpose of the study, the population size and how much time and resources are available.
4
What sampling method involves dividing a population into subgroups and sampling from each group?
Common mistakes
There are several common mistakes to avoid when tackling statistics problems:
- Confusing central tendency measures, such as mixing up mean, median and mode. Each measure presents a different aspect of the data, so mixing up the measure leads to incorrect interpretation.
- Incorrect graphs, including mislabelling an axis or using the wrong scales. This can be as harmful if not worse as it changes the data's message and your resulting conclusions.
- Sampling errors can skew results e.g. using a non-representative sample or a biased sampling method.
- Check your work. It is a simple mistake, but students don't always double-check their results, conscious of the exam clock and eager to move on to the next problem. This is particularly risky with multi-step calculations.
5
What error is the most common cause of misinterpreting the data in a graph?
Conclusion
Statistics provides us with skills for data analysis and interpretation. We can measure central tendency and data representation methods by understanding topics like data types. It's important to choose the sampling method that is best suited to your task and avoid the common mistakes we discussed.
TeachTutti has verified and DBS-checked GCSE Maths tutors who can support your revision for exams in this and related topics. You can also test your understanding of statistics and the subject in general with GCSE Maths past papers.
