Q.State and explain the main characteristics of statistics (as data).

Not every set of numbers is 'statistics' — Secrist's definition lists the features a set of figures must possess to qualify.

Statistics must be an aggregate (not a single number), quantitative, accurate, systematically collected for a fixed purpose, affected by many causes, and comparable.

Following Horace Secrist's definition, a set of figures qualifies as statistics only if it has the following characteristics.

1. Aggregate of facts. A single, isolated figure ('Ram earns ₹20,000') is not statistics; only an aggregate that can be compared and related (the earnings of all 200 workers) is.
2. Affected by multiplicity of causes. Statistical facts result from many causes acting together — a firm's sales depend on price, advertising, season, competition and income simultaneously.
3. Numerically expressed. Statistics are quantitative; qualitative statements ('the students are intelligent') are not statistics until expressed in numbers.
4. Enumerated or estimated to reasonable accuracy. Data may be counted exactly (census) or approximated (sample), but any estimation must meet reasonable standards of accuracy — a careless guess does not qualify.
5. Collected systematically. Data must be gathered through a planned, orderly, unbiased procedure; haphazard figures are unreliable.
6. Collected for a predetermined purpose. The purpose must be fixed before collection, since it decides what to collect and how; aimless data is usually unusable.
7. Placed in relation to each other (comparable). Figures must be homogeneous — relating to the same phenomenon, unit and definition — so they can meaningfully be compared over time, place or group.

Data failing any of these tests — a lone number, a purely qualitative statement, or haphazard non-comparable figures — is not statistics in the disciplined sense.

Students often omit 'comparability' and 'predetermined purpose', which are among the most frequently tested characteristics. Another error is giving examples that are actually single figures — a single number can never illustrate the 'aggregate of facts' characteristic.