National Year 10 Statistics
Chapters: 2
1. 1. The collection of data
1a Planning · 1b Types of data · 1c Population and sampling · 1d Collecting data
- The Scientific Method – The scientific method is the careful way scientists find out how the world works. Observe something, ask a testable question, make a hypothesis (a clear, testable guess), test it with a fair experiment (change one variable, measure one, keep the rest the same), repeat and record data, analyse it, draw a conclusion and share it so others can check. Results that fail the test are useful too: they send you back to a new hypothesis.
- Collection of Data: Primary and Secondary Sources, Sampling, Census of India and NSSO – Data can be primary (collected first-hand by you) or secondary (already collected by someone else). Primary data comes from personal interviews, mailed questionnaires or telephone interviews. We may study everyone (census) or a small part (sample). Samples can be random or non-random. Results can have sampling errors and non-sampling errors. In India, the Census counts everyone every 10 years, and the NSSO (now NSO) runs sample surveys.
- Sampling: Learning About a Population from a Sample – A population is the whole group we want to know about; a sample is a smaller part we actually check. A good sample is chosen at random so that it represents the population. Simple random sampling gives everyone an equal chance; stratified sampling takes the right share from each group; systematic sampling takes every k-th item. Different samples give slightly different answers (sampling variation), but bigger samples wobble less (law of large numbers). A biased sample gives a wrong answer however big it is.
2. 2. Processing, representing and analysing data (part 1)
2a Tabulation, diagrams and representation · 2b Measures of central tendency · 2c Measures of dispersion · 2d Further summary statistics
- Statistics: Asking Questions, Averages and Stacked Bar Graphs – Statistics starts with a question that has many possible answers. We collect data, organise it, show it in a graph, and find one number that sums it up. The mean is the fair share, the median is the middle value, and the mode is the most common value. A weighted average gives more importance to some values. Stacked and 100% stacked bar graphs show how a whole is split into parts.
- Measures of Dispersion: Range, Mean Deviation, Variance and SD – Dispersion means spread: how far the values sit from the centre. Range = largest − smallest. Mean deviation = average distance from the mean (or median). Variance = average of squared distances from the mean. Standard deviation = √variance. The same ideas work for grouped data when every term is multiplied by its frequency.
- Index Numbers: Simple Aggregative Method, WPI, CPI, IIP, Uses and Inflation – An index number is a number that shows how much something (like prices or output) has changed compared with a base year, whose index is 100. The simple aggregative price index is ΣP1 ÷ ΣP0 × 100. Weighted indices give more importance to items bought more. India's key indices are the Consumer Price Index (CPI) for retail prices, the Wholesale Price Index (WPI) for wholesale prices and the Index of Industrial Production (IIP) for factory output. The inflation rate is the percentage rise in a price index over a year.