The symbol is used to represent
A the variance of the sample
B the variance of the population
C the standard deviation of the sample
D the standard deviation of the population
The correct answer and explanation is:
The correct answer is:
D) the standard deviation of the population
The symbol σ (Greek letter sigma) is used to represent the standard deviation of a population in statistics. This is a measure of the amount of variation or dispersion in a population data set. If the values in a data set are close to the mean, the standard deviation is small. If they are spread out over a wider range, the standard deviation is larger.
Standard deviation is used to quantify how much individual data points in a population differ from the population mean (denoted by μ). When you are dealing with the entire population, you use σ for standard deviation and σ² for population variance.
In contrast, when working with a sample (a subset of the population), a different symbol is used. The standard deviation of a sample is represented by s, and the variance of the sample is s².
Understanding whether a statistic refers to a sample or a population is very important. This determines which formulas and symbols to use. For example, calculating the population standard deviation involves dividing by N (the number of values in the population), whereas the sample standard deviation uses n – 1 in the denominator to account for the degrees of freedom.
In summary, σ specifically refers to the standard deviation of a population. It is one of the most important tools in descriptive statistics and helps in understanding the spread or dispersion of a full data set. Recognizing this symbol and knowing what it represents is essential for accurate data analysis and interpretation.