Statistical Officer / Government Statistical Service (GSS) Assessment Descriptive Statistics, Data Analysis and Modelling Syllabus

Descriptive Statistics, Data Analysis and Modelling syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Descriptive Statistics, Data Analysis and Modelling in Statistical Officer / Government Statistical Service (GSS) Assessment, not a summary of it.

1. 1

   Summarising Data

   3 topics

   • Types of data
     • Categorical, ordinal, interval and ratio data
     • Cross-sectional, time series and panel data
   • Measures of central tendency and spread
     • Mean, median and mode and when each is appropriate
     • Range, interquartile range, variance and standard deviation
     • Skewness and kurtosis
   • Data visualisation
     • Histograms, box plots and scatter plots
     • Choosing the right chart for the message
     • Avoiding misleading visualisations
2. 2

   Relationships Between Variables

   3 topics

   • Correlation
     • Pearson and Spearman correlation coefficients
     • Correlation does not imply causation
   • Linear regression
     • Simple linear regression and least squares
     • Interpreting coefficients, R-squared and residuals
     • Multiple regression and confounding
   • Model assumptions and diagnostics
     • Linearity, homoscedasticity and normality of residuals
     • Multicollinearity and influential observations
3. 3

   Index Numbers and Time Series

   3 topics

   • Index numbers
     • Laspeyres and Paasche price indices
     • Rebasing and chain-linking
     • Real versus nominal values and deflation
   • Time series components
     • Trend, seasonality, cycle and irregular components
     • Seasonal adjustment concepts
   • Forecasting basics
     • Moving averages and exponential smoothing
     • Interpreting and communicating forecast uncertainty
4. 4

   Analytical Reasoning with Data

   3 topics

   • Identifying patterns and anomalies
     • Outlier detection and treatment
     • Spotting data entry and processing errors
   • Drawing valid conclusions
     • Confounding, lurking variables and Simpson's paradox
     • Ecological fallacy and aggregation effects
   • Reproducible analysis (conceptual)
     • Reproducible Analytical Pipelines (RAP) principles
     • Version control and documentation of analysis

Descriptive Statistics, Data Analysis and Modelling flashcards for Statistical Officer / Government Statistical Service (GSS) Assessment

19 of 61 cards from the Descriptive Statistics, Data Analysis and Modelling deck — real questions with worked answers.

1. What are the four main types (levels) of measurement for data?

   Nominal (categories, no order), Ordinal (ordered categories, unequal/unknown intervals), Interval (ordered, equal intervals, no true zero, e.g. temperature in °C), and Ratio (equal intervals with a true zero, e.g. height, weight).

2. Distinguish categorical (qualitative) data from numerical (quantitative) data, and give the two subtypes of each.

   Categorical splits into nominal (unordered) and ordinal (ordered). Numerical splits into discrete (countable values, e.g. number of children) and continuous (any value in a range, e.g. weight).

3. What is the difference between discrete and continuous numerical data?

   Discrete data take separate, countable values (often integers, e.g. number of cars). Continuous data can take any value within a range and are measured rather than counted (e.g. time, length).

4. Define cross-sectional, time series, and panel (longitudinal) data.

   Cross-sectional: many units observed at a single point in time. Time series: one unit observed over many time points. Panel/longitudinal: many units observed over multiple time points (combines both).

5. State the formula for the arithmetic mean of a sample $x_1,\dots,x_n$.

   $$\bar{x} = \frac{1}{n}\sum_{i=1}^{n} x_i$$

6. How do you find the median of a dataset, and why is it preferred over the mean for skewed data?

   Order the values; the median is the middle value (or the mean of the two middle values if $n$ is even). It is preferred for skewed data because it is robust to outliers and extreme values, unlike the mean.

7. Define the mode and state for which type of data it is the only valid measure of central tendency.

   The mode is the most frequently occurring value. It is the only valid measure of central tendency for nominal (categorical) data.

8. State the formula for the sample variance $s^2$.

   $$s^{2} = \frac{1}{n-1}\sum_{i=1}^{n}(x_i - \bar{x})^{2}$$

9. Why does the sample variance divide by $n-1$ rather than $n$?

   Dividing by $n-1$ (Bessel's correction) gives an unbiased estimator of the population variance; using $n$ underestimates it because the sample mean is used in place of the unknown population mean, removing one degree of freedom.

10. How is the standard deviation related to the variance, and why is it often preferred?

    The standard deviation is the square root of the variance, $s = \sqrt{s^{2}}$. It is preferred because it is expressed in the same units as the original data, making it more interpretable.

11. Define the interquartile range (IQR) and explain why it is a robust measure of spread.

    $\text{IQR} = Q_3 - Q_1$, the range of the middle 50% of the data. It is robust because it ignores the lowest and highest 25% of values, making it insensitive to outliers.

12. What is the coefficient of variation (CV) and when is it useful?

    $$\text{CV} = \frac{s}{\bar{x}} \times 100\%$$ It expresses spread relative to the mean, allowing comparison of variability between datasets with different units or very different means.

13. Define skewness and describe the relative positions of mean, median and mode for a right (positive) skew.

    Skewness measures asymmetry of a distribution. For right (positive) skew, the tail extends to the right and typically $\text{mode} < \text{median} < \text{mean}$.

14. What does kurtosis measure, and what is the excess kurtosis of a normal distribution?

    Kurtosis measures the heaviness of the tails / peakedness of a distribution. A normal distribution has kurtosis $3$, i.e. an excess kurtosis ($\text{kurtosis}-3$) of $0$.

15. Which chart type is most appropriate for showing the distribution of a single continuous variable?

    A histogram, which groups continuous data into bins and shows frequency by bar height (with no gaps between bars).

16. What is the key difference between a bar chart and a histogram?

    A bar chart displays categorical data with gaps between bars (order arbitrary); a histogram displays continuous data in ordered, adjacent bins with no gaps, and area/height represents frequency.

17. What does a box-and-whisker plot display, and how are outliers typically defined on it?

    It shows the minimum, $Q_1$, median, $Q_3$, and maximum (five-number summary). Outliers are commonly points beyond $Q_1 - 1.5\times\text{IQR}$ or $Q_3 + 1.5\times\text{IQR}$.

18. Which visualisation is best for examining the relationship between two continuous variables?

    A scatter plot, which plots paired observations as points and reveals the form, direction, and strength of any association.

19. List three principles of good data visualisation (avoiding misleading charts).

    Start bar-chart axes at zero, keep aspect ratios honest, label axes and units clearly, avoid chart junk / 3D distortion, and use appropriate chart types for the data. (Any three.)

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