To calculate the population proportion:
\[ P = \frac{X}{N} \times 100 \]
Where:
A population proportion describes the ratio or percentage of a population that has a certain characteristic. It is calculated by dividing the number of successes by the population size and then multiplying by 100 to express it as a percentage.
No, a population proportion cannot be negative because the values for both the number of successes and the population size cannot be less than zero.
No, they are different. A population proportion describes the percentage of a population with a certain characteristic, while standard deviation describes the variance from the mean in a set of data.
It represents the ratio of individuals or items in a population with a specific characteristic, often expressed as a percentage.
Use population mean when analyzing characteristics with varying amounts, and use population proportion when measuring characteristics in binary terms (e.g., presence or absence of a trait).
Example 1:
Assume a survey was conducted with 200 participants, and 50 of them indicated that they prefer to work remotely.
Using the formula:
\[ P = \frac{50}{200} \times 100 = 25\% \]
The population proportion of people who prefer to work remotely is 25%.
Example 2:
In a classroom of 30 students, 12 students have completed their homework.
Using the formula:
\[ P = \frac{12}{30} \times 100 = 40\% \]
The population proportion of students who have completed their homework is 40%.
