Statistics 1

Worked examples (5)

• 1State the stages of the statistical modelling cycle (4 marks, S1)
• 2Advantages and limitations of statistical modelling (4 marks, S1)
• 3Refining a model after data collection (5 marks, S1)
• 4Modelling assumptions in context — coin tosses (4 marks, S1)
• 5From raw data to a model — choosing a distribution (5 marks, S1)

Worked examples (5)

• 1Mean from a grouped frequency table (4 marks, S1)
• 2Variance and SD using the shortcut formula (5 marks, S1)
• 3Quartiles by linear interpolation (6 marks, S1)
• 4Coding — find original mean and SD (5 marks, S1)
• 5Compare two data sets — choose statistics (5 marks, S1)

Worked examples (5)

• 1Forward probability $P(X u003e a)$ (4 marks, S1)
• 2$P(a u003c X u003c b)$ (5 marks, S1)
• 3Inverse — find $x$ given $P(X u003c x) = p$ (5 marks, S1)
• 4Find $\\mu$ and $\\sigma$ from two probabilities (7 marks, S1)
• 5Use the normal model in context (5 marks, S1)

Worked examples (5)

• 1Histogram — frequency density and missing frequency (6 marks, S1)
• 2Box plot with outliers (6 marks, S1)
• 3Median, quartiles and percentile from a cumulative frequency curve (6 marks, S1)
• 4Back-to-back stem-and-leaf and a comparison (7 marks, S1)
• 5Skewness coefficient and shape interpretation (5 marks, S1)

Worked examples (5)

• 1Addition rule with Venn diagram (5 marks, S1)
• 2Conditional probability and independence (6 marks, S1)
• 3Tree diagram with conditional probabilities (7 marks, S1)
• 4Venn diagram with three sets (7 marks, S1)
• 5Mutually exclusive vs independent (4 marks, S1)

Worked examples (5)

• 1Find the constant in a PMF and compute $E(X)$ (5 marks, S1)
• 2Variance of $X$ and of a linear transform (6 marks, S1)
• 3Discrete uniform distribution — derive $E$ and $\\text{Var}$ (6 marks, S1)
• 4Cumulative distribution function $F$ (5 marks, S1)
• 5Construct a PMF from a context — coin tosses (7 marks, S1)

Worked examples (5)

• 1Product-moment correlation coefficient $r$ (5 marks, S1)
• 2Regression line of $y$ on $x$ (6 marks, S1)
• 3Correlation does not imply causation (4 marks, S1)
• 4Effect of coding on $r$ and on the regression line (6 marks, S1)
• 5Extrapolation and limits of linearity (5 marks, S1)