Introduction to statistics and probability

Introduction to statistics and probability

Statistics-is a mathematical science pertaining to the collection, presentation, analysis and interpretation of data.

An analysis of any situation can be done in two ways

• Statistical analysis
• Non-statistical analysis

Statistical analysis- it is the science of collecting, exploring and presenting large amounts of data to identify patterns and trends. It is also called quantitative analysis.

Non-statistical analysis-it provides generic information and includes text, sound, still images and moving images. It is also called qualitative analysis.

There are two major categories of statistics

1. Descriptive statistics
2. Inferential statistics

Descriptive statistics helps organizing data and focuses on the main characteristics of the data. It also provides a summary of the data numerically or graphically.

Inferential statistics generalizes the larger dataset and applies probability theory to draw a conclusion. It allows you to infer population parameters based on samples statistics and to model relationships within the data.

Differences between descriptive and inferential.

Descriptive statistics

1. Organizing and summarizing data using numbers and graphs.
2. Data summary-bar graphs, histograms, pie charts etc. shape of the graph and skewness.
3. Measures of central tendency; mean, median and mode.
4. Measures of variability; range, variance and standard deviation.

Inferential statistics

1. Using sample data to make an inference or draw a conclusion of the population.
2. Uses probability to determine how confident we can be that the conclusions we make are correct (confidence intervals & margins of error).

Statistics are characteristics that describe a sample.

Parameter are characteristics that describe a population.

Sample is a sub-set of the population.

Scale of measurement.

Nominal scale data

1. Qualitative /categorical
2. Names, colours, labels, gender etc.
3. Order does not matter.

Ordinal scale data

1. Ranking/placement.
2. The order matters.
3. Difference cannot be measured.

Interval scale data

1. The order matters
2. Difference can be measured (except ratios)
3. No true ‘0’ starting point.

Ratio scale data

1. The order matters.
2. Differences are measurable (including ratios)
3. Contains a ‘’0’’ starting point