Which is the correct form of the relative frequency formula? I could find the answer on google so may a jiskha math expert might know.
a) RF=1/(sigma root(2pi))e^-(1/2 (x-u)^2 /sigma^2) or b) RF=1/(sigma root(2pi))e-(1/2 ((x-u)^2 )/sigma^2)
b) RF=1/(sigma root(2pi))e-(1/2 ((x-u)^2 )/sigma^2) is the correct form of the relative frequency formula.
The correct form of the relative frequency formula is b) RF=1/(sigma√(2π))e^(-(1/2)((x-u)^2)/(sigma^2)).
In this formula:
- RF refers to the relative frequency.
- σ represents the standard deviation.
- π is the mathematical constant pi.
- e is the mathematical constant approximately equal to 2.71828.
- (x-u) is the difference between the observed value x and the mean u.
To determine the correct form of the relative frequency formula, let's break down the formulas (a) and (b) that you've provided.
In statistics, the relative frequency formula is typically used to calculate the probability density function (PDF) of a normal distribution. The PDF represents the likelihood of a random variable falling within a specific range of values.
Formula (a): RF = 1 / (σ √(2π)) e^(-1/2 (x - μ)^2 / σ^2)
Formula (b): RF = 1 / (σ √(2π)) e^(-1/2 ((x - μ)^2) / σ^2)
Both formulas are similar and share the common elements for the PDF of a normal distribution. Let's discuss these elements to determine the correct form:
1. RF: It represents the relative frequency or the probability density function.
2. μ: It denotes the mean or the average value of the random variable.
3. σ: This symbolizes the standard deviation, which measures the dispersion or spread of the values around the mean.
4. x: It represents the specific value within the distribution for which you want to calculate the probability density.
5. e: It is the mathematical constant Euler's number, approximately 2.71828, used as the base of the natural logarithm.
At first glance, both formulas seem to be almost identical. However, upon closer examination, there is a subtle difference: the placement of parentheses.
The correct form, based on commonly used mathematical notation, is formula (a):
RF = 1 / (σ √(2π)) e^(-1/2 (x - μ)^2 / σ^2)
Therefore, the correct version should be:
RF = 1 / (σ √(2π)) e^(-1/2 (x - μ)^2 / σ^2)
It's always important to double-check any formulas, especially ones related to specialized topics such as mathematics, to ensure their accuracy and appropriateness for your specific context.