Final answer:
The population standard deviation is calculated using the formula σ = √(Σ(x-μ)² / N). It measures the spread of data in a population by taking the square root of the average squared deviations from the mean.
Step-by-step explanation:
To find the population standard deviation, you must first understand the difference between a population and a sample. A population includes every member of a set, whereas a sample consists of a part of the population. The formula to calculate the population standard deviation (σ) involves using the population mean (μ) and is shown as:
σ = √(Σ(x-μ)² / N)
Where:
- σ is the population standard deviation
- x represents each value in the population
- μ is the population mean
- N is the number of items in the population
After calculating the variance (σ²), which is the average of the squared deviations from the mean, the population standard deviation is the square root of this variance. To calculate the mean, add all the values together and divide by the number of values. The deviations are the differences between each value and the mean. Finally, you square these deviations, sum them up, and divide by N to find the variance. The square root of the variance gives you the population standard deviation.