Question

reasoning there are 75 vehicles in a parking lot. the frequency table shows data about the types and colors of the vehicles. complete a relative frequency table to show the distribution of the data with respect to color. use pencil and paper. explain why the first two numbers in each row must add up to 100%.

Explanation:

Step1: Calculate relative frequency for blue row

Relative frequency formula: $\text{Relative Frequency}=\frac{\text{Frequency}}{\text{Row Total}}\times100\%$.
For blue - car: $\frac{22}{41}\times 100\%\approx53.7\%$.
For blue - truck: $\frac{19}{41}\times 100\%\approx46.3\%$.

Step2: Calculate relative frequency for red row

For red - car: $\frac{18}{34}\times 100\%\approx52.9\%$.
For red - truck: $\frac{16}{34}\times 100\%\approx47.1\%$.

Step3: Calculate relative frequency for total row

For total - car: $\frac{40}{75}\times 100\%\approx53.3\%$.
For total - truck: $\frac{35}{75}\times 100\%\approx46.7\%$.

The first two numbers in each row must add up to $100\%$ because we are looking at the distribution of vehicle types (car and truck) within each color group (blue, red). The sum of all parts (car and truck) of a whole (a particular color group) is $100\%$.

Answer:

Color	Car	Truck	Total
Red	$52.9\%$	$47.1\%$	$100\%$
Total	$53.3\%$	$46.7\%$	$100\%$