Calculating Error Bars for Height and Time in Ball Drop Experiment

• aron silvester
In summary, the conversation discusses conducting an experiment to measure the time and height of a dropped ball from different levels. The data collected is used to plot a graph in Excel, but the question arises about calculating the error bars for the X axis. The speaker's partner suggests multiplying the standard deviation by the average time, but the speaker is unsure about this method. They also mention that for the Y axis, the error bar can be calculated using the standard deviation or a constant multiple of it. However, since the X axis involves a quadratic term, the same method cannot be applied.
aron silvester
1. The problem statement, all variables, and given/known data
• Take the ball and drop it from chest level 5 times recording the times and the height. Do this same procedure once again for knee, waist, and eye level. You should now have four data points for your height and four data points for the time, each with uncertainty estimates. We used the average (calculated in the Collecting data section below) of the times to plug in the t variable in the X column for each level. MY QUESTION IS, HOW DO I CALCULATE THE THE ERROR BAR ALONG THE X AXIS? I already know the error bar along the Y axis (height), my group member
• Collecting data
• Data set: Similar to Table 3

Homework Equations

The end goal is to plot a graph on excel that looks something like the image below. I have both the X and Y values, but I just need to figure out the error bars for the X axis.

aron silvester said:
HOW DO I CALCULATE THE THE ERROR BAR ALONG THE X AXIS?
How did you calculate them for the Y axis?

haruspex said:
How did you calculate them for the Y axis?
My partner just eyed the uncertainty when she measured the height (height is used as the y-axis later for the graph) from which to drop the ball. My partner said in order to get the uncertainty for the x-axis, she multiplied the standard deviation by the average times. For example, to get the error bar for the knee level she multiplied the average time for knee-level, 0.244, and multiplied it with the standard deviation of 0.0622. These measurements are recorded in the Collecting Data of my post. Does that make sense? Isn't the error bar just the standard deviation? I'm not sure why she's multiplying it by the average.

For Y, I would take the standard deviation, or some constant multiple of it, like 2 or 3, as the error bar length. Certainly makes no sense to multiply by the average.
But as the text says, it is a bit different for the X axis because of the quadratic term. For that you should use the same constant multiplier as you used for the Y, and multiply by the actual t reading (not the average).

1. How do I calculate error bars for height and time in a ball drop experiment?

To calculate error bars for height and time in a ball drop experiment, you will need to first determine the standard deviation of your data points. This can be done using a statistical software or by hand. Once you have the standard deviation, you can then calculate the error bars by multiplying the standard deviation by a factor, such as 1.96 for a 95% confidence interval, and then adding and subtracting this value from the mean.

2. What is the purpose of using error bars in a ball drop experiment?

The purpose of using error bars in a ball drop experiment is to represent the uncertainty or variability in your data. They provide a visual representation of the range of values that your data points could potentially fall within, taking into account the standard deviation and the confidence interval chosen.

3. How do I interpret error bars in a ball drop experiment?

Interpreting error bars in a ball drop experiment involves understanding the range of values that they represent. The length of the error bars can indicate the amount of uncertainty in the data, with longer bars representing a larger range of values. Additionally, if the error bars overlap between two data points, it suggests that there is not a significant difference between them.

4. Can error bars be used to make conclusions about the data in a ball drop experiment?

Error bars should not be used on their own to make conclusions about the data in a ball drop experiment. They should be used in conjunction with other statistical tests and measures to draw accurate conclusions. Additionally, the size and variability of the error bars should be taken into account when interpreting the results.

5. Are there any limitations to using error bars in a ball drop experiment?

One limitation to using error bars in a ball drop experiment is that they assume a normal distribution of the data. If the data is not normally distributed, alternative methods may need to be used to represent the variability in the data. Additionally, error bars do not take into account any systematic errors that may be present in the experiment.

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