Question

A student made five successive measurements to determine the density of copper.He obtained the following values: rho1= 9.9 g/cm3, rho2 = 7.8 g/cm3, rho3 = 9.1 g/cm3, rho4 = 9.6 g/cm3,and rho5 = 10 g/cm3.

1) Calculate the average density rhoave=

2)Calculate the standard deviation σN−1(rho) =

3) Calculate uncertainty in density measurement Δrho =

4) State the percent variability in the density measurement: percent variability = _%

5) Given the accepted (known) density of copper to be rhocu = 8.96 g/cm3, what is the percent difference in the density measurement: percent difference =_%

Answer 1

Answer:

1)  X = 9.28 g / cm³   2) σ = 0.803  g/cm³ 3) Δρ = σ = 0.8 g / cm³

Explanation:

1) The average value of a measurement is the medical data values ​​among the number of them

     X = Σ xi / n

Let's calculate

   X = = (9.9 + 7.8 + 9.1 + 9.6 + 10) / 5

   X = 9.28 g / cm³

2) the formula for standard deviation

           σ = √(Σ (xi- X)²/n )

   σ = √ [(9.9-9.28)² + (7.8-9.28)² + (9.1-9.28)² + (9.6-9.28)² + (10-9.28)²] / 5

   σ =√ [0.3844 + 2.19 + 0.0324 + 0.1024 +0.5184] / 5 = √ [3.2276 / 5]

   σ = 0.803  g/cm³

3)   As a measurement series of the same amount was performed, the uncertainty is the standard deviation

      Δρ = σ = 0.8 g / cm³

4) This is the standard deviation between the percent measure

          percent variability = σ/X   100%

          percent variability=   0.803 / 9.28  100

          variability = 8.6%

5) The percentage difference

         Er% = (X -X real) / X real 100

         Er% = (9.28 -8.96) / 8.96 100

         Er%= 3.6%