IEB Grade 12 Statistics Cheat Sheet

Statistics is about 20 marks of Paper 2. Calculator skills plus clear interpretation in words.

Centre and spread

• Mean $\bar{x}=\frac{\sum x}{n}$; grouped: $\frac{\sum f{x}_{\text{mid}}}{n}$.

• Standard deviation: read ${\sigma }_x$ from the calculator. Variance $={\sigma }^2$.

• Adding a constant shifts the mean only. Multiplying every value by $k$ multiplies the mean by $k$ and $\sigma$ by $|k|$.

Five-number summary and box plots

• Min, $Q_1$, median, $Q_3$, max. IQR $=Q_3-Q_1$.

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

• Positive skew: long right tail, mean $>$ median. Negative skew: long left tail, mean $<$ median.

• Comparing: centre (median), spread (IQR, range), shape (skew), always in words.

Ogives

• Plot cumulative frequency at the upper boundary; start at 0 on the first lower boundary.

• Read $Q_1$ at $\frac{n}{4}$, median at $\frac{n}{2}$, $Q_3$ at $\frac{3n}{4}$.

Regression and correlation

• Calculator A+BX gives $\hat{y}=a+bx$.

• $r$ runs from $-1$ to $1$. The closer $|r|$ is to 1, the stronger the linear relationship; near 0 means little or no linear relationship. Describe strength in words and in context.

• Interpolation (inside the data) is reliable; extrapolation is not.

• Correlation does not prove cause.

Know by heart

• Calculator steps for $\bar{x}$, $\sigma$, $a$, $b$ and $r$

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

On the formula sheet

• $\bar{x}$, ${\sigma }^2$ and the regression line formulae

Common traps

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

• Plotting ogive points at midpoints.

• Describing skew by where the data bunches instead of the tail.

• Swapping $a$ and $b$ in the regression equation.