GCSE Statistics Revision Notes - Key Methods, Data Types and Calculations

Sep 5, 2026

GCSE Statistics revision notes covering core topics from collecting data to interpreting results. The material explains sampling methods such as random, stratified, systematic, cluster, quota and convenience sampling, plus census. It compares primary vs secondary data, quantitative vs qualitative, continuous vs discrete, and details questionnaires including open and closed questions and pilot surveys. Further sections address mean, standard deviation, variance, standardised scores, normal distribution, scatter diagrams, causal relationships, Spearman’s rank correlation and index numbers with practical examples.

LanguageEnglish

CategoryExam

FormatPDF

Pages10

Reading Time25 min

AccessFree to download

Collecting data

Sampling methods

Census

Types of data

Primary and secondary data

Quantitative and qualitative data

Continuous and discrete data

Questionnaires

Open vs closed questions

Pilot survey

Calculations

Mean from frequency and grouped data

Standard deviation and variance

Standardised scores

Normal distribution

Scatter diagrams and line of best fit

Causal relationships

Spearman’s rank correlation

Index numbers

Chain base index numbers

Weighted means

GCSE Statistics Revision notes Collecting data Sample – This is when data is collected from part of the population. There are different methods: Random sampling, Stratified sampling, Systematic sampling, cluster sampling, Quota sampling, Convenience sampling Random sample – Where each piece of data has an equal chance of being picked. Methods Random number table – Tables of random numbers can be used. Here is an extract from a table of random numbers 36015 37672 90153 67480 26237 10635 34269 01638 Split the numbers into to digit numbers 36 01 53 76 72 90 15 36 74 80 26 23 71 06 35 34 26 90 16 38 And then start from 36 and select numbers between 0 and 50 36 01 15 36 26 Leave out any numbers above 50 (in this case) Calculator – Use the RAN button on your calculator. For numbers from 0 to 100 type 100 Shift RAN Until you have enough numbers. Numbers in a bag, internet random number generator etc Stratified sample – Where the data sampled is in proportion to the population. Example: The table shows the number of students in a school Year Students 7 120 8 100 9 115 10 125 Total 460 A stratified sample of size 30 is to be taken. How many year 7s will be picked? Solution: Fraction of year 7 students in school is 120 240 120 x 30 = 7.82… so approx 8 year 7 students will be picked 240 Other Sample techniques Convenience sample – the first so many pieces of data in the list are sampled. (Quick but unlikely to be representative. ) Quota sample – The amount or quota of each group is given eg 100 woman were sampled Systematic sampling – Data is chosen at regular intervals eg Every 10th Person. Cluster sampling – The population is divided into groups (cluster) and then a group is chosen at random. Census – This is when all of the data in the population is taken. For example a census of the entire population of the UK is taken every 10 years. | | Advantage | Disadvantage | | --- | --- | --- | | Sample | Cheaper | Not completely representative | | | Less time consuming | Possibly biased | | | Less data to be analysed | | | Census | Unbiased | Time consuming | | | Accurate | Expensive | | | Takes account of whole population | Difficult to ensure whole population is used. | Types of Data Primary data-This is data collected by the person doing the analysis Advantage-Should be reliable. Disadvantage – Collecting is time consuming. Secondary data – This is data that has been collected by someone else. Advantage-No need to collect. Ready to analyse. Disadvantage – Could be unreliable Quantitative data – This is data that has numerical values. (Time, heights, weights, number of people) Qualitative data-This is data that is not numerical (Colour, type) Continuous Data – This is data that is on a continuous scale (Lengths, height, weights, measurements) Discrete Data-This data that consists of separate numbers. (Shoe sizes, number of people, money) Questionnaires Open questions – Has no suggested answers and gives people chance to reply as they wish Advantage –Allows for a range of answers Disadvantage – Range of response too broad-hard to analyse Closed questions – Gives a set of answer for the person to choose from Advantage – Restricts response making it easy to analyse responses Disadvantage – Will not necessarily cover all responses Pilot survey (pre-test)– Small scale replica of the survey to be carried out. Used to ensure that the method of Data collection / questionnaire and data required is suitable for the bigger survey. Leading question – Avoid questions that infer an opinion such as “Smoking is bad for you”,“Do you agree?” Calculations Mean from frequency table Example Mean from grouped data Find the mid-point of each group and then multiply by frequency. Sum and then divide by total frequency Example Standard Deviation Variance is a measure of spread about the mean of a distribution of data. The square root of the variance is the

FAQs

What is the difference between random sampling and stratified sampling?

Random sampling gives each data item an equal chance of being selected. Stratified sampling takes data in proportion to the population, such as selecting students from each year group based on their counts.

How do you find the mean for grouped data?

Find the midpoint of each group, multiply each midpoint by its frequency, sum the results, then divide by the total frequency.

What is standard deviation and how is it related to variance?

Variance measures the spread of data about the mean. Standard deviation is the square root of the variance.

Sep 5, 2026

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