Making the Grade

Learning Focus

Analyze grade data with means, weighted averages, and the effect of outliers.

Big idea

• Mean of $n$ scores: sum $\div\ n$.
• Weighted average: multiply each score by its weight (as a decimal) and add.
• To reach a target mean, find the total needed and subtract the total so far.
• A very low score can pull the mean down; the median may represent a typical grade better.

Worked example

Tests count $40\%$ and homework $60\%$. Test $90$, homework $80$:

$0.4(90)+0.6(80)=36+48=84$.

To average $85$ over $4$ tests with $82,88,80$ so far: need total $340$; have $250$; need $90$.

Takeaways

• Weights must sum to 100%.
• Target total = target mean $\times$ count.
• Check for outliers before choosing mean or median.