Question

1. the table shows the relationship between a runner’s average speed and the average number of steps the runner takes each second.

speed (feet per second) | steps (steps per second)
16.00 | 3.00
17.00 | 3.10
17.50 | 3.20
18.50 | 3.25
20.00 | 3.40
21.00 | 3.50
22.00 | 3.60
23.00 | 3.75
24.00 | 3.80
24.50 | 3.90

a. identify the explanatory and response variables.

b. construct a scatterplot using the data. be sure to label the axes and the graph.

grid for scatterplot with x and y axes

c. what relationship seems to exist between the runner’s average speed and their average steps per second?

d. explain the meaning of the point (23.00, 3.75).

Explanation:

Part (a)

Step1: Recall Variable Definitions

Explanatory variable (independent) is what we think causes change, response (dependent) is what we measure.

Step2: Analyze the Data

Speed (feet per second) is likely the explanatory variable (we might think speed affects steps), steps (steps per second) is the response variable (it responds to speed changes).

Step1: Set Axes

• x - axis: Label "Speed (feet per second)", range from 16 to 25 (to cover data: 16.00–24.50).
• y - axis: Label "Steps (steps per second)", range from 3 to 4 (to cover data: 3.00–3.90).

Step2: Plot Points

For each (Speed, Steps) pair: (16.00, 3.00), (17.00, 3.10), (17.50, 3.20), (18.50, 3.25), (20.00, 3.40), (21.00, 3.50), (22.00, 3.60), (23.00, 3.75), (24.00, 3.80), (24.50, 3.90). Mark these coordinates on the grid.

Step1: Analyze Trend

Look at the scatterplot (or data: as speed increases, steps increase).

Step2: Determine Relationship Type

The pattern shows a positive association (both variables increase together) and likely linear (points follow a roughly straight - line trend).

Answer:

Explanatory variable: Runner’s average speed (feet per second).
Response variable: Average number of steps per second.

Part (b)