Given : A random sample of five Galaxy 8 smartphones is selected from the production line after final assembly, and the result of the weight control measurement is (in grams) are :
X= 155.1, 154.8, 155.5, 155.3, and 154.6.
here, n=5
The average weight :[tex]\overline{x}=\dfrac{\sum^{i=5}_{i=1}x_i}{n}[/tex]
[tex]=\dfrac{155.1+154.8+155.5+155.3+154.6}{5}\\\\=\dfrac{775.3}{5}=155.06[/tex]
∴ Average weight ([tex]\overline{x}[/tex])=155.06 grams
Uncertainty = Standard deviation: [tex]\sigma=\sqrt{\dfrac{\sum^{i=5}_{i=1}(x_i-\overline{x})^2}{n}}[/tex]
[tex]=\sqrt{\dfrac{(0.04)^2+(-0.26)^2+(0.44)^2+(0.24)^2+(-0.46)^2}{5}}[/tex]
[tex]=\sqrt{\dfrac{0.532}{5}}=\sqrt{0.1064}=0.326190128606\approx0.33[/tex]
i.e. Its uncertainty : [tex]\sigma=0.33[/tex]
The fractional uncertainty = [tex]\dfrac{\sigma}{\overline{x}}[/tex]
[tex]=\dfrac{0.33}{155.06}=0.00212820843544\approx0.002[/tex]
