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The content for this section is sub-divided
into the following areas:
Measures of location
Top
| Foundation
tier |
Higher tier |
Notes |
Resources |
| Mean, median and mode for raw
data.
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Use of change of origin when
calculating the mean.
Effect on the average of changes in the sample,
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eg the addition or withdrawal
of a sample member.
eg the mean of the numbers 1003, 1005, 1006, and 1009
is equal to 1000 plus the mean of 3, 5, 6 and 9. |
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| Mean, median and mode for
discrete frequency distributions.
Modal class for grouped frequency distributions.
Median for grouped frequency distributions.
Mean for grouped frequency distributions. |
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Graphical methods of
obtaining the median will be acceptable.
Candidates may make use of a linear change of scale
when calculating the mean.
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| Advantages and disadvantages
of each of the three measures of location in a given situation. |
Reasoned choice of a measure
of location appropriate to the nature of the data and the purpose of the
analysis. |
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Geometric mean. |
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Measures of spread
Top
| Foundation
tier |
Higher tier |
Notes |
Resources |
| Range. |
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| Quartiles for discrete data.
Quartiles and percentiles, for grouped frequency
distributions. |
Deciles. |
Graphical methods will be
accepted. |
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| Interquartile range for
discrete and continuous data. |
Interpercentile ranges. |
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Variance and standard
deviation. |
Divisor n. To include grouped
frequency distributions.
Efficient use of a calculator should be encouraged. |
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| Advantages and disadvantages
of each of these measures of spread. |
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| Construction of box and
whisker plots.
Use of box and whisker plots to identify outliers.
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An outlier is defined as an
observation less than Q1 - 1.5 (Q3 - Q1) or greater than Q3 + 1.5 (Q3 -
Q1), where Q1 and Q3 are the lower and upper quartiles respectively. |
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Calculation and
interpretation of standardised scores. |
Only general interpretation
is expected. |
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| Use of tabulated data,
diagrams, measures of location and measures of spread to compare data
sets. |
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Use of standardised scores to
compare values from different frequency distributions. |
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Other summary statistics
Top
| Foundation
tier |
Higher tier |
Notes |
Resources |
| Simple index numbers.
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Weighted index numbers.
Chain base numbers.
General Index of Retail Prices. (RPI). |
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W
weighted index |
| Crude rates. |
Standardised rates. |
For example, birth,
death, unemployment. |
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Time series
Top
| Foundation
tier |
Higher tier |
Notes |
Resources |
| Drawing a trend line by eye
and using it for prediction. |
Evaluating and plotting
appropriately chosen moving averages. |
Trend lines will not be
required to pass through the mean. |
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| Identification of seasonal
variation.
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Trend line based on moving
averages.
Seasonal effect at a given data point.
Average seasonal effect.
Prediction of future values. |
Graphical methods only will
be expected. |
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Quality assurance
Top
| Foundation
tier |
Higher tier |
Notes |
Resources |
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Plotting sample means,
medians or ranges over time to view consistency and accuracy against a
target value. |
To include looking for
indications where the process is off target or of an increase in
variability. |
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Correlation and regression
Top
| Foundation
tier |
Higher tier |
Notes |
Resources |
| Scatter diagrams. Recognition
by eye of positive correlation, negative correlation, lack of correlation. |
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| The distinction between
correlation and causality. |
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Spearman’s rank correlation
coefficient as a measure of agreement; its calculation and limitation in
interpretation. |
Includes the case of tied
ranks.
Calculations for large samples will not be expected.
The formula for Spearman’s rank correlation coefficient will be given. |
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| Fitting a straight line by
eye through mean to the plotted points on a scatter diagram. |
Obtaining the equation of the
fitted line in the form y=mx+c; the interpretation of m and c.
Non-linear data. |
Includes discussion of
whether such a straight line is appropriate.
A ‘suggested’ relationship will be given |
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| Interpolation and
extrapolation. |
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Including the dangers of
inappropriate extrapolation. |
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| Interpretation of bivariate
data presented in the form of a scatter diagram.
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Comparison of the degree of
correlation between two or more pairs of data sets with reference to
scatter diagrams and/or rank correlation coefficients. |
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Estimation
Top
| Foundation
tier |
Higher tier |
Notes |
Resources |
| Estimation of population mean
from a sample.
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Estimation of a population
proportion from a sample; the use of this method of estimation in opinion
polls.
Variability in estimates from different samples and
the effect of sample size.
Estimation of population size based on the
capture/recapture method.
An elementary quantitative appreciation of
appropriate sample size. |
Higher Tier : eg to include
the concept that to halve the variability in an estimate, four times the
sample size is required. |
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