Applying statistical methods
What's covered
Key facts
Estimation and capture-recapture
Summary statistics estimate population characteristics, e.g. about half the population will be above the sample median.
Index numbers
The base year always has an index number of 100.
Lines of best fit and regression
The double mean point is (x-bar, y-bar), the mean of the x-values and the mean of the y-values.
Quality assurance and control charts
If a sample value lies between a warning line and an action line, another sample is taken straight away.
Rates of change
Birth rate = (number of births / total population) x 1000.
Scatter diagrams and correlation
AQA treats correlation values of 0.6 or above (or -0.6 or below) as strong, 0.2 up to but not including 0.6 (or -0.2 down to but not including -0.6) as weak, and values strictly between -0.2 and 0.2 as no correlation; "moderate" is not required.
Spearman's rank and Pearson's correlation coefficients
To decide which variable gives the best estimate, use the one whose PMCC is closest to 1 (strongest linear correlation).
Time series and moving averages
A cyclic pattern is a rise and fall that is not of a fixed period (often linked to economic cycles and usually lasting at least 2 years), whereas seasonal variation always has a fixed, known period.
Estimation and capture-recapture
Capture-recapture assumes the population does not change between samples (no births, deaths or migration).
Index numbers
A chain base index number compares each value with the value one period earlier: (this year's value / last year's value) x 100.
Practice questions with answers
A taste of the 85 questions in this topic, answers marked. Sign up to practise the full set with spaced repetition.
In the Petersen capture-recapture formula, what number is the denominator?
- •Number of animals in the second sample
- •Number of animals marked in the first sample
- ✓Number of marked animals in the second sample
- •Total number of animals caught altogether
A price index for 2024 is 112, with 2020 as the base year. What does this mean?
- •Prices fell by 12% from 2020 to 2024
- •Prices rose by 112% from 2020 to 2024
- ✓Prices rose by 12% from 2020 to 2024
- •Prices were £112 higher in 2024 than 2020
To draw a more accurate line of best fit by hand, which calculated point should the line pass through?
- ✓The double mean point
- •The highest plotted point
- •The midpoint of the x-axis
- •The origin (0, 0)
On a control chart for sample means, where are the warning lines drawn?
- •1 standard deviation either side of the target
- ✓2 standard deviations either side of the target
- •3 standard deviations either side of the target
- •At the highest and lowest sample means
Why are standardised birth rates used instead of crude birth rates to compare two towns?
- •Crude rates are only used for deaths
- •Crude rates cannot be found from tables
- •Standardised rates ignore the population size
- ✓The towns may have different age structures
Which representation is most appropriate for bivariate data such as the heights and arm spans of students?
- •Comparative pie chart
- •Cumulative frequency graph
- ✓Scatter diagram
- •Stem and leaf diagram
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