Introduction to Statistics
Introduction to Statistics covers how business data are collected, organised and presented before any calculation. The exam tests the distinction between primary and secondary data, census and sample methods, classification, tabulation and the construction of frequency distributions and simple charts.
Core rules
- Primary data are collected first-hand for the current purpose; secondary data already exist and must be checked for reliability, coverage and definitions.
- Census covers every unit; sampling studies a representative part. A good sample is unbiased and large enough, and the sampling method must be stated.
- Classification groups data by a common characteristic; tabulation arranges them in rows and columns with a clear title, units, totals and source.
- In an exclusive frequency distribution, classes such as 10–20, 20–30 have no gaps and the upper limit is excluded. Class mark = (lower + upper)/2; class width = upper − lower.
- Presentation should suit the data: bar charts for categories, histograms for continuous grouped data, line graphs for time series, pie charts for shares of a whole.
Worked example
Twenty daily sales figures (₹ hundreds) are 12, 18, 15, 22, 25, 19, 14, 28, 31, 17, 23, 26, 20, 16, 24, 29, 21, 27, 13, 30. Using classes 10–20, 20–30 and 30–40, the frequencies are 8, 10 and 2 respectively. For example, 10–20 contains 12, 18, 15, 19, 14, 17, 16 and 13; 20 is counted in 20–30, not 10–20, because the upper limit is excluded. The class marks are 15, 25 and 35, and the total frequency is 20, matching the number of observations.
Traps
- Overlapping classes such as 10–20 and 20–30 without a stated rule for the boundary value.
- Unequal class widths that make a histogram misleading.
- Using secondary data without checking the year, area or definition.
- Drawing a pie chart when the categories are not parts of one whole.