Answer:
Kindly check explanation
Step-by-step explanation:
Given the following instructions :
Choose 4 numbers from the whole numbers 0 - 10
Note : Repetition is allowed
Choose 4 numbers with the smallest possible standard deviation.
The smallest possible value of standard deviation obtainable is 0;
Hence in other to obtain a standard deviation value of 0, then;
The mean squared deviation value must be zero (0)
Σ(X - mean)^2 = 0
To achieve this, the values of X and the mean must be the same.
Hence all 4 numbers (X) must be the same in other to have a mean value which is equal to X
For instance :
If X = 3, 3, 3, 3 (since Repetition is allowed)
Man value = (3+ 3+ 3+ 3) / 4 = 12 / 4 = 3
Σ(3 - 3)² = 0 for all values of x
√Σ(x - mean)² / n = 0 ; if all values of x are the Same
n = Number of observations
A possible list of values is (3,3,3,3)
or -0.375
