Explanation:

The given statement is "For any two numbers SD is always"

SD stands for Standard Deviation which is a measure of the dispersion of a set of data values.

The options given are:

a) Twice the range
b) Half of the range
c) Square of the range
d) None of these

Range is the difference between the maximum and minimum values of a set of data.

To understand the relationship between SD and range, we need to know the formula for calculating SD.

Formula for calculating SD:

SD = √[(∑(x - μ)²)/n]

where,
x = data values
μ = mean of the data
n = number of data values

From this formula, we can see that SD depends on the deviation of each data value from the mean.

Now, let's consider the options given:

a) Twice the range:
Range = maximum value - minimum value
SD = √[(∑(x - μ)²)/n]
There is no direct relationship between range and SD. So, option (a) is incorrect.

b) Half of the range:
Range = maximum value - minimum value
SD = √[(∑(x - μ)²)/n]
There is no direct relationship between range and SD. So, option (b) is incorrect.

c) Square of the range:
Range = maximum value - minimum value
SD = √[(∑(x - μ)²)/n]
There is no direct relationship between range and SD. So, option (c) is incorrect.

d) None of these:
As we have seen above, there is no direct relationship between range and SD. So, option (d) could be the correct answer.

Conclusion:

None of the options given is correct. Therefore, the correct answer to the question is "None of these".