Math Problem Statement

Completa esas tablas y corrígela así es necesario

Completa esas tablas y corrígela así es necesario

Solution

I can see the tables you've provided with calculations. Let's work on completing them.

We have the following data for each table:

Table 2.2 (Pipette Measurements)

Given:

  • ΣPa=97.3\Sigma Pa = 97.3
  • Σ(PaXˉ)2=0.2631\Sigma (Pa - \bar{X})^2 = 0.2631

To calculate:

  • Mean Xˉ=ΣPan\bar{X} = \frac{\Sigma Pa}{n}
  • Variance S2=Σ(PaXˉ)2n1S^2 = \frac{\Sigma (Pa - \bar{X})^2}{n-1}
  • Standard deviation S=S2S = \sqrt{S^2}

For n=10n = 10:

  • Xˉ=97.310=9.73\bar{X} = \frac{97.3}{10} = 9.73
  • S2=0.2631101=0.26319S^2 = \frac{0.2631}{10-1} = \frac{0.2631}{9}
  • S=S2S = \sqrt{S^2}

Table 2.3 (Probeta Measurements)

You need to calculate the sums and complete the table similarly:

  • ΣPa\Sigma Pa
  • Σ(PaXˉ)2\Sigma (Pa - \bar{X})^2

I'll proceed with these calculations next.It seems like I can’t do more advanced data analysis right now. Please try again later.

However, here are the steps you can follow to complete the calculations manually:

Table 2.2 (Pipette Measurements)

  • Mean Xˉ=ΣPan=97.310=9.73\bar{X} = \frac{\Sigma Pa}{n} = \frac{97.3}{10} = 9.73
  • Variance S2=Σ(PaXˉ)2n1=0.263190.02923S^2 = \frac{\Sigma (Pa - \bar{X})^2}{n-1} = \frac{0.2631}{9} \approx 0.02923
  • Standard deviation S=S20.029230.171S = \sqrt{S^2} \approx \sqrt{0.02923} \approx 0.171

Table 2.3 (Probeta Measurements)

You would follow a similar process:

  1. Add up all the PaPa values to get ΣPa\Sigma Pa.
  2. Compute the mean Xˉ\bar{X} for the data.
  3. Calculate (PaXˉ)2(Pa - \bar{X})^2 and sum these values.
  4. Finally, calculate the variance and standard deviation as shown in Table 2.2.

If you'd like, I can walk you through completing these calculations in detail.

Would you like assistance on the next steps or any specific part? Here are some related questions for further practice:

  1. How would you interpret the standard deviation in this context?
  2. What are the steps to calculate variance from raw data?
  3. How do these results help compare the accuracy of both instruments?
  4. What impact does sample size have on standard deviation?
  5. How would the results change if an outlier was introduced?

Tip: When calculating variance, always remember to use n1n - 1 (for sample variance) to correct for bias in small datasets.

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Math Problem Analysis

Mathematical Concepts

Statistics
Data Analysis

Formulas

Mean (X̄) = ΣPa / n
Variance (S^2) = Σ(Pa - X̄)^2 / (n - 1)
Standard Deviation (S) = √S^2

Theorems

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Suitable Grade Level

Grades 10-12