A simple random sample of 100 observations was taken from a large population. The sample mean and the standard deviation was determined to be 80 and 12, respectively. The standard error of mean is _______
Concept:
No of observations
\(N = {\left( {\frac{{{C_V}}}{ϵ}} \right)^2}\)
Where,
ϵ = allowable % error of mean
Cv = coefficient of variation.
\(C_v= \frac{\sigma}{\bar{x}}~\times 100\)
σ = Standard deviation, x̅ = Mean
Calculation:
Given:
x̅ = 80, σ = 12, N = 100
\(C_v= \frac{\sigma}{\bar{x}}~\times 100\)
\({C_v} = \frac{{12}}{{80}} × 100\)
Cv = 15%
\(N = {\left( {\frac{{{C_V}}}{ϵ}} \right)^2}\)
\(100 = {\left( {\frac{{{15}}}{ϵ}} \right)^2}\)
ϵ = 1.5%
The standard error of mean = mean × percentage of absolute mean error = \(80\times {{1.5} \over 100}\) = 1.2
Important Questions from Statistical Variables
In a class of 50 students, the marks obtained are
Marks
15
30
37
40
45
48
No. of students
2
8
14
12
10
4
Its median is
Let X be a normal random variable with mean zero and variance 9. If a = P(X ≥ 3) then P(|X| ≤ 3) equals:
Find the median if the given data set is:
3, 3, 7, 8, 12, 13, 16, 19
A machine produces 0, 1 or 2 defective pieces in a day with an associated probability of \(\frac{{1}}{{6}}\), \(\frac{{2}}{{3}}\) and \(\frac{{1}}{{6}}\) respectively. The mean value and the variance of the number of defective pieces produced by the machine in a day, respectively, are
The median of 7, 5, 8, x, 12, 17 is 10, then what is the value of x?
