Answer:
1A. 20.5
2A. 14.54
1B. 14.625
2B. quite good reasonable
Step-by-step explanation:
Mean is used to measure central tendency (i.e. representative of data) and standard deviation is use to measure dispersion of data. The formula use to calculate mean and variance is :
[tex]Mean(bar{x}) = \dfrac{Sum of all the observations}{Total number of observation}[/tex]
[tex]Standard deviation(\sigma) = \sqrt{\frac{1}{n} \sum_{i=1}^{n}(x_{i}-\bar{x})^2}[/tex]
1A. Mean of six sample =
[tex]= \dfrac{Sum of all the observations}{Total number of observation}[/tex]
⇒ [tex]\dfrac{36+14+21+39+11+2}{6}[/tex]
⇒ Mean = 20.5
Standard deviation of six sample =
[tex] = \sqrt{\frac{1}{6}[ (36-20.5)^2+(14-20.5)^2+(21-20.5)^2+(39-20.5)^2+(11-20.5)^2+(2-20.5)^2}][/tex]
⇒ σ = 14.54
2A. Total number of error = 36 + 14 + 21 + 39 + 11 + 2 = 123
Total number of error made by all scans is 123 error per 6000 scans.
1B. Mean of all 12 samples is:
[tex]= \dfrac{Sum of all the observations}{Total number of observation}[/tex]
⇒ [tex]\dfrac{36+14+21+39+11+2+33+45+34+17+1+29}{12}[/tex]
⇒ Mean = 23.5
Standard deviation of all 12 samples =
[tex] = \sqrt{\frac{1}{12}[ (36-23.5)^2+(14-23.5)^2+(21-23.5)^2+(39-23.5)^2+(11-23.5)^2+(2-23.5)^2+(33-23.5)^2+(45-23.5)^2+(34-23.5)^2+(17-23.5)^2+(1-23.5)^2+(29-23.5)^2}][/tex]
⇒ σ = 14.625
2B. Taking small sample instead of large sample can be quite risky sometimes as larger sample give us more accurate result than small sample.
But here we can take a small sample because the mean of both the size of the sample is near about.
