I worked in a lab group with Mayleen Mori, Jeffrey Joseph, and Mary Robert. In this laboratory our lab group measured the rate at which we jumped (jumps per second) and the total number of jumps (jumps) until a miss.
We did not know enough about this system in advance to make a prediction on the likely mathematical relationship.

Equipment

Jump ropes

Stopwatches

Procedure

Mayleen jumped rope while Jeffrey used a stopwatch to time Mayleen's jumps. I counted the total number of jumps until Mayleen missed. Mary recorded our data. Mayleen jumped at six different rates from a slowest rate of 0.32 jumps per second to a fastest rate of 2.10 jumps per second.

Data table

Jump rate (jumps/s)

Jumps (jumps)

0.32

10.00

0.74

22.00

1.09

34.00

1.63

66.00

1.87

68.00

2.10

79.00

Data chart

Analysis

The data plots roughly close to a straight line. Based on the data our group made the following analysis:

There is a mathematical relationship between the jump rate and total number of jumps.

The mathematical relationship is linear.

The y-intercept is not necessarily zero.

The slope was found using the SLOPE function. The slope was 40.48 jumps/(jumps/s).

The y-intercept was found using the INTERCEPT function. The y-intercept was 5.79 jumps.

The mathematical relationship for this system is given by the equation:
jumps = 40.48 (jumps per second) ‒ 5.79

Note that in other laboratories the relationship might be linear with a y-intercept of zero or non-linear. There is also the possibility that there is no relationship. If the relationship is linear with a y-intercept of zero, then the LINEST function is used to the find the slope.

Conclusion

Our group found a linear relationship between the jump rate and the total number of jumps. The total number of jumps can be predicted from the jump rate.

There was some measurement uncertainty in measuring the time for the jumps. We stopped the timer only when Mayleen missed a jump. This means that the last jump happened before the stopwatch was stopped. Our times will all be slightly longer than the actual length of time for the number of jumps. This time difference affects every measurement in the same manner, thus the conclusion that a linear mathematical relationship exists is not affected by the uncertainty.

Another area of concern is that only Mayleen jumped.
Another jumper might produce different results.
Our mathematical relationship might not be exactly the same for other jumpers.
A future improvement might to use a larger number of jumpers.