The following are advantages of standard deviation EXCEPT that it

Analyze the question: The question asks for the statement that is NOT an advantage of the standard deviation. Four options describe strengths of the standard deviation, and one describes a weakness or is false.

Concept: The standard deviation measures how spread out data values are around the mean. It is the square root of the variance:

σ = √[Σ(x − x̄)² / n]

Its main strengths are:

• It uses every value in the data set in its calculation.
• It is algebraically and mathematically sound. It can be manipulated further, for example in combining groups or in the normal distribution.
• It is the most widely used measure of dispersion.
• It is the basis of many statistical tests (t-test, z-test, correlation, regression) and of sampling theory. It is also the most stable measure from sample to sample.

Checking each option:

• A. Greater practical utility in sampling. This is true, so it is an advantage.
• B. It uses all values in its calculation. This is true, so it is an advantage.
• C. It is useful in analysing the t-test. This is true, so it is an advantage.
• D. It is not a sound mathematical index. This is false. The standard deviation is a sound mathematical index, so this is not an advantage. It is the exception.
• E. It is the most popular measure of dispersion. This is true, so it is an advantage.

The standard deviation is mathematically sound, so saying it is "not a sound mathematical index" cannot be an advantage.

Exam tip: In "EXCEPT" questions, look for the option that says something negative about a concept that is known for its strengths. Remember the standard deviation as "uses all values, mathematically sound, used in sampling and tests."