Data Interpretation
🔒 Log in to trackmedium importance~2 Q in Tier 119 formulas⚡ 10 shortcuts5 subtopics
Every formula in this topic, grouped by subtopic. Print it and pin it above your desk.
Reading tables: totals, differences, ratios
Row total
\text{total} = \sum \text{row cells}
Row average
\bar{x} = \frac{\text{row total}}{\text{number of columns}}
Cell ratio
\text{ratio} = a : b \text{ (reduced)}
Rate from counts
\text{rate} = \frac{\text{passed}}{\text{appeared}} \times 100\%
Percentage change and comparisons
Percentage change
\frac{\text{new}-\text{old}}{\text{old}} \times 100\%
Base = the old / original value.
Share
\frac{\text{part}}{\text{whole}} \times 100\%
Points vs percent
\text{points} = a - b; \quad \%\text{age} = \frac{a-b}{b} \times 100
Pie charts: degrees, shares and totals
Slice value
\text{value} = \frac{\theta}{360} \times \text{total}
theta is the slice angle in degrees.
Angle to percent
\% = \frac{\theta}{3.6}
Percent to angle
\theta = \% \times 3.6
Part to angle
\theta = \frac{\text{part}}{\text{total}} \times 360
Per-degree value
1° = \frac{\text{total}}{360}
Averages from data
Simple average
\bar{x} = \frac{\sum x}{n}
Weighted average
\bar{x} = \frac{\sum n_i x_i}{\sum n_i}
n_i is the count in each band or row.
Entry to hit a target average
x = (n+1)\bar{x}_{new} - n\bar{x}_{old}
Growth rates and successive changes
Growth multiplier
\text{new} = \text{old}\left(1+\frac{r}{100}\right)
Successive growth
r_{total} = \left(1+\frac{a}{100}\right)\left(1+\frac{b}{100}\right)-1
Reverse to original
\text{old} = \frac{\text{new}}{1+\frac{r}{100}}
Total multiplier
\frac{\text{end}}{\text{start}} = 1 + \frac{r_{total}}{100}