Additional assessable quantitative skills
- Syllabus
- 2018
- Topic
- —
- Level
- A2
Learning objectives
Levels, changes and rates of change
The level of a variable is its measured value at a point or during a period. A change in level says how far that value moved; a rate of change says how quickly it moved relative to a starting value or to time.
\text{absolute change}=\text{new level}-\text{old level}\qquad %\text{ change}=\frac{\text{new}-\text{old}}{\text{old}}\times100
| Statement | What it means |
|---|---|
| output rises from 100 to 104 | the level increases by 4 |
| output growth is 4% | the level increases at a rate of 4% |
| growth falls from 4% to 2% | output still rises, but more slowly |
| growth becomes -2% | the level falls by 2% over the stated period |
On a time-series graph, the vertical position shows the level while the slope indicates the absolute rate of change. A rising line can become flatter: the level is still increasing even though its rate of increase is falling.
A fall in a positive growth rate is not necessarily a fall in the variable itself. Keep level, absolute change, percentage change and percentage-point change separate, and always state the time interval and starting base.
How composite indicators combine evidence
A composite indicator combines several component indicators into one summary measure. It can represent a multidimensional idea, such as development, that no single statistic captures adequately.
The components must first be put on a comparable scale, often by converting each to an index. A stated weighting rule then gives each component its influence, and the normalised values are aggregated into the composite. The method, coverage, date and direction of every component must remain visible when the result is interpreted.
| Strength | Limitation |
|---|---|
| summarises several dimensions in one comparable value | chosen components and weights reflect value judgements |
| supports ranking and tracking change over time | aggregation can hide a very weak component or offset it against a strong one |
| can communicate a complex pattern clearly | national averages conceal inequality and data quality may differ |
The Human Development Index is a composite indicator because it combines normalised health, education and income dimensions. Its overall score is useful for comparison, but the separate dimension scores are still needed to diagnose why two countries with similar totals differ.
Raw quantities measured in years, currency and rates cannot simply be added. This is an IA2 skill: understand both the information gained by aggregation and the assumptions and detail lost when many indicators become one number.
What seasonal adjustment removes
A seasonally adjusted figure is a time-series value from which an estimated recurring seasonal pattern has been removed. The adjustment makes adjacent periods more comparable when predictable calendar effects would otherwise obscure underlying movement.
Statisticians use repeated observations across years to estimate effects associated with seasons or the calendar, such as holiday spending, harvests or regular school-year hiring. They subtract or divide out that estimated component, depending on the statistical model, while preserving the series' units.
| Raw movement | Seasonally adjusted reading |
|---|---|
| retail sales rise every December | removes the normal December lift before comparing with November |
| agricultural employment rises each harvest | removes the recurring harvest effect before judging the underlying labour trend |
| an unusual strike reduces output | remains an irregular event; it is not a seasonal pattern |
Use adjusted values for month-to-month or quarter-to-quarter comparisons of the underlying movement. Use unadjusted values when the actual level in that season matters, for example planning December stock or staffing.
Seasonally adjusted does not mean inflation-adjusted, trend-free or corrected for every shock. The trend, business cycle and irregular events can remain, and revised data may change the estimated seasonal pattern as new observations arrive.