Help please statistics

Question

1A - Candidate Ames and Candidate Burton are both running for mayor in a small town. Early polling results for Candidate Ames are displayed below. Calculate the absolute and relative change in the percentage of voters who support this candidate. 

MonthAugustSeptember
Percentage of Eligible Voters	Who Prefer Candidate Ames	12.0%	15.8%

Absolute change:  = 3.8 percentage points

Percentage change (rounded to one decimal place): = ? %

Answer 1

Hello Susan,

Let X be any variable. Here are some definitions. (In the following definitions, i stands for "initial" and f stands for "final".)

i) Absolute Change (in X) = X_f - X_i

ii) Relative Change = (X_f - X_i)/X_i

The relative change expresses the change in X in relation to the original value of X. It is typically expressed as a fraction or decimal. However, it is often convenient to convert the relative change to the percentage change (by multiplying by 100%). That is,

iii) Percentage Change = [(X_f - X_i)/X_i]·100%

Therefore, the percentage change you require is

Percentage change = [(15.8% - 12.0%)/12.0%]·100%

= 31.7% (rounded to the first decimal place.)

Hope that helps! Let me know if you need any further explanation.

William