Answer & Solution
Answer: Option
A
Solution:
Understanding Standard Deviation:
Standard deviation tells us how spread out a set of numbers is. A small standard deviation means the numbers are clustered close together, while a large standard deviation means they are more spread out.
Calculating Standard Deviation (Simplified):
1. Find the average (mean) of the numbers. In this case, the average of 3, 3, 3, 5, 5, 5 is (3+3+3+5+5+5)/6 = 4
2. Find the difference between each number and the average. For example: 3 - 4 = -1, 5 - 4 = 1
3. Square each of those differences. This gets rid of the negative signs. (-1)² = 1, 1² = 1
4. Find the average of the squared differences. This is called the variance.
5. Take the square root of the variance. This is the standard deviation.
Applying it to the Question:
Let's do the calculation for the given numbers (3, 3, 3, 5, 5, 5):
* Average = 4
* Differences from the average: -1, -1, -1, 1, 1, 1
* Squared differences: 1, 1, 1, 1, 1, 1
* Average of squared differences (variance): (1+1+1+1+1+1)/6 = 1
* Square root of variance (standard deviation): √1 = 1
Therefore, the standard deviation is 1.
The correct answer is A.
Note: The unit of measurement doesn't affect the calculation of standard deviation; it only affects the units of the final answer.
