# Evaluating minimum and maximum values with calculations

• crememars
In summary: No, that would not be correct. You would need to use the uncertainty in the measurements to get the smallest possible speed.
crememars
Homework Statement
Determine the maximum and minimum values for the average speed of an object falling from a height of 2 meters in 0.63 seconds.

Uncertainty of time = +/- 0.05 s
Uncertainty of height = +/- 0.02 m
Relevant Equations
v = ∆y/∆t
Hi! I know this may seem like a silly question but I really just want to make sure I understand this correctly. I've already calculated the minimum and maximum values for time and height:

t min = 0.58 s
t max = 0.68 s
y min = 1.98 m
y max = 2.02 m

To calculate the minimum average speed, would I use the minimum values of time and height ? (and vice versa for max speed)
I thought that would be the process, but the minimum values give a bigger speed, and the max values give me a smaller speed:

v measured = 2.00/0.63 = 3.17 m/s
v min = 1.98/0.58 = 3.41 m/s
v max = 2.02/0.68 = 2.97 m/s

This is really confusing..

If you want ##\bar{v}_{min}## you have to choose the uncertainties such that the quantity: $$\bar{v} = \frac{ h \pm u_h}{t \pm u_t}$$ is as small as it can be.

How would you choose the signs to do that?

PeroK
v = ∆y/∆t .

erobz said:
If you want ##\bar{v}_{min}## you have to choose the uncertainties such that the quantity: $$\bar{v} = \frac{ h \pm u_h}{t \pm u_t}$$ is as small as it can be.

How would you choose the signs to do that?
addition gives the smallest value.. so I'd essentially be using the maximum values to get a minimum value for speed? that's very weird haha

crememars said:
addition gives the smallest value.. so I'd essentially be using the maximum values to get a minimum value for speed? that's very weird haha
You have you think about the relative sizes of the numerator and denominator. Think about what happens in the division. Addition is not the answer, it depends on which part (numerator, denominator) you are talking about?

crememars
erobz said:
You have you think about the relative sizes of the numerator and denominator.
Wait, would it be correct to divide the minimum distance by the maximum time then? Ohh it makes a bit more sense now, I see how that would produce a minimum speed

hmmm27 and erobz

## 1. What is the purpose of evaluating minimum and maximum values with calculations?

The purpose of evaluating minimum and maximum values with calculations is to determine the range of possible values for a given set of data. This can help in identifying outliers, understanding the spread of the data, and making informed decisions based on the data.

## 2. How do you calculate the minimum and maximum values of a set of data?

To calculate the minimum value, you can arrange the data in ascending order and select the first value. To calculate the maximum value, you can arrange the data in descending order and select the first value. Alternatively, you can use mathematical formulas such as the minimum function (MIN) and maximum function (MAX) in spreadsheet software.

## 3. Can minimum and maximum values change with different calculations?

Yes, the minimum and maximum values can change depending on the type of calculation being performed. For example, if you are calculating the minimum and maximum values of a set of data using different statistical measures such as mean or median, the values may differ from the ones calculated using a simple range calculation.

## 4. How can evaluating minimum and maximum values with calculations be useful in data analysis?

Evaluating minimum and maximum values with calculations can be useful in data analysis as it provides a quick overview of the data and helps in identifying any extreme values or trends. It can also help in detecting errors or anomalies in the data and making data-driven decisions.

## 5. Are there any limitations to evaluating minimum and maximum values with calculations?

Yes, there are some limitations to evaluating minimum and maximum values with calculations. It may not always provide a complete picture of the data, especially if there are a large number of outliers. Additionally, it may not be suitable for certain types of data such as categorical data or data with missing values.

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