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The standard deviation of six numbers 3, 3, 3, 5, 5, 5 is

A. 1

B. 4

C. 0

D. Cannot be obtained since the unit of measurement is not given

Answer: Option A

Solution (By Examveda Team)

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.

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Comments (1)

  1. Virat Yadav
    Virat Yadav:
    1 year ago

    Wrong .. the answer will be option A
    Simply find the sd it will be 1

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