# Exploring Why Method 2 is More Precise than Method 1

• arierreF
In summary, Method 2 is more precise than method 1 because it calculates the value of mean for each group, resulting in a smaller standard deviation. This is due to the fact that the standard deviation of the mean values is smaller than the standard deviation of the individual measurements. This is further supported by the formula σ2 = (√10)σ1 for method 2, showing that the standard deviation decreases as the number of groups increases.
arierreF
First of all, as you can see I'm new in forum. Sorry if i am posting in wrong section.

Problem: A student measure the times 100 times.
Method 1:
He calculates the mean X and the standard deviation $\sigma$.
Method 2:
Now the student, divides the 100 measurements in 10 groups.
He calculates the value of mean to each group. Therefore he calculates the standard deviation (with the 10 values corresponding to the mean of each group).

Question:

Why the method 2 is more precise than the method 1?

Attempt:

In my experimental results, i observe that method 2 has a small standard deviation. Ok so i can conclude that method 2 is more precise because we have a small uncertainties.

But why this happens? If we divided in four intervals, the stranded deviation would be smallest. but why??

Method 2 is not more accurate than method 1.

Let σ = α1 for method 1. Let σ2 = std deviation of one of the ten averaged samples. Let σ3 = std deviation of the ten averaged samples.

Then σ2 = (√10)σ1 but σ3 = (1/√10)σ2
= (1/√10)(√10)σ1 = σ1.

rude man said:
Method 2 is not more accurate than method 1.

Let σ = α1 for method 1. Let σ2 = std deviation of one of the ten averaged samples. Let σ3 = std deviation of the ten averaged samples.

Then σ2 = (√10)σ1 but σ3 = (1/√10)σ2
= (1/√10)(√10)σ1 = σ1.

With my experimental results, with method 1 i calculated the standard deviation σ for the 100 measurements.

With method 2, i divided the 100 measurements in 10 random groups. Then i obtained 10 means.

The standard deviation of the 10 mean values, is smaller than the standard deviation of the 100 measurements.

## 1. Why is Method 2 considered more precise than Method 1?

Method 2 is considered more precise than Method 1 because it has a smaller margin of error. This means that the results obtained from Method 2 are closer to the true value compared to Method 1.

## 2. What factors contribute to the precision of a scientific method?

The precision of a scientific method is influenced by several factors such as the equipment used, the skill and experience of the scientist, the size of the sample, and the control of variables.

## 3. How does the sample size affect the precision of a method?

A larger sample size usually results in a more precise method. This is because a larger sample size reduces the effect of random errors and provides a more representative data set.

## 4. Can Method 1 still be useful even though it is not as precise as Method 2?

Yes, Method 1 can still be useful in certain situations. It may be more cost-effective or easier to perform, especially when the difference in precision between the two methods is negligible.

## 5. Is precision the only factor to consider when evaluating a scientific method?

No, precision is just one of the factors to consider when evaluating a scientific method. Other important factors include accuracy, repeatability, and the validity of the results.

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