The standard error of the sample mean is 1.1793
The approximate standard deviation of a statistical sample population is known as the standard error (SE). By utilizing standard deviation, the standard error is a statistical concept that assesses how accurately a sample distribution represents a population.
The given humidities are 55 62 63 63 76
Do we have to find the standard error of the sample mean =?
The formula for the standard error is
SE = σ/n
The mean value is
x = (∑i[tex]x_{i}[/tex] )/n
= (55+62+63+63+76)/5
= 319/5
= 63.8
Now the standard deviation is
σ = √((∑i〖([tex]x_{i}[/tex] -μ)〗^2 )/(n-1))
= √(〖(53-63.8)〗^2+〖(62-63.8)〗^2+...........+〖(76-63.8)〗^2 )/(5-1)
= √((-116.64-3.24-0.64-0.64+148.84)/4)
= √(27.86/4)
= √6.92
= 2.630
The value of standard error is
SE = σ/√n
= 2.630/√5
= 2.630/2.230
= 1.1793
Therefore the standard error is 1.1793
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