Question

This is a standard deviation contest. You must choose four numbers from the whole numbers 0 to 10 , with repeats allowed. (a) Choose four numbers that have the smallest possible standard deviation. What is s in this case? (Enter your answer rounded to the nearest whole number.)

Answer 1

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)