IEB Grade 11 Statistics Cheat Sheet

Statistics is about 20 marks of Grade 11 Paper 2. Graphs, spread and shape in one place.

Grouped data

• Histogram: bars touch. Frequency polygon: plot at midpoints and close at both ends.

• Estimated mean $=\frac{\sum f{x}_{\text{mid}}}{n}$. Modal class: highest frequency.

Ogives

• Cumulative frequency at the upper boundary, starting at 0.

• $Q_1$ at $\frac{n}{4}$, median at $\frac{n}{2}$, $Q_3$ at $\frac{3n}{4}$, $k$th percentile at $\frac{k}{100}n$.

Variance and standard deviation

• ${\sigma }^2=\frac{\sum (x-\bar{x}{)}^2}{n}$, $\sigma =\sqrt{{\sigma }^2}$; calculator: ${\sigma }_x$.

• Within one standard deviation: count values with $\bar{x}-\sigma \le x\le \bar{x}+\sigma$.

• Add a constant: mean shifts, $\sigma$ unchanged.

Box plots, skewness and outliers

• Five-number summary: min, $Q_1$, median, $Q_3$, max.

• Outlier: beyond $Q_1-1,5\times$ IQR or $Q_3+1,5\times$ IQR.

• Positive skew: long right tail, mean $>$ median. Negative skew: the opposite.

• Outliers pull the mean much more than the median.

Know by heart

• Calculator steps for $\bar{x}$ and ${\sigma }_x$

• Skewness rules (the outlier rule is given in the question)

On the formula sheet

• Mean and variance formulas

Common traps

• Plotting ogives at midpoints.

• Using $s_x$ instead of ${\sigma }_x$.

• Gaps between histogram bars.