Unbiased Estimate for Population Parameters

Calculate the unbiased estimates of population mean and variance for the following samples:

1. Sample size \(=100\), \(\sum{x}=160\), \({{\sum{x}}^{2}}=265\)
2. \(n=250\), \(\sum{x}=43,205\), \(\sum{{{x}^{2}}}=7,469,107\)
3. Sample size\(=50\), \(\sum{(x}-10)=328\), \({{\sum{x}}^{2}}=16062\)
4. Sample size\(=34\), \(\sum{(x}+2)=103\), \({{\sum{x}}^{2}}=1167\)
5. \(n=200\), \(\sum{\left( t-300 \right)}=2012\), \(\sum{{{\left( t-300 \right)}^{2}}}=22526\)
6. \(n=150\), \(\sum{\left( t-100 \right)}=2000\), \(\sum{{{\left( t-100 \right)}^{2}}}=35600\)
7. Sample size\(=150\), \(\sum{(x}-170)=-2250\), \({{\sum{(x-154)}}^{2}}=11000\)
8. Sample size\(=50\), \(\sum{(x}-150)=3600\), \(\sum{(x}-190{{)}^{2}}=65000\)