Frequency Distribution in Statistics

Study Notes

Frequency refers to the number of occurrences of a value in a given series of observations.
Frequency distribution is a table that organizes data by showing the values of a variable with their corresponding frequencies.
The left column of a frequency distribution table includes numerical intervals of a variable under study, while the right column contains the list of frequencies.
Class-limits or class-intervals are formed within two values, with the lower value being the lower class limit and the upper value being the upper class limit.

The difference between the upper and lower class limits is called the class length or class width.
Class length/width = Upper class limit – Lower class limit.

A continuous frequency distribution is a type of frequency distribution where the variable takes values expressed in class intervals within certain limits.
Example: Marks obtained by 20 students in an exam for 50 marks can be converted into a continuous frequency distribution.

Sampling is a process used in statistical analysis where a predetermined number of observations are taken from a larger population.
The methodology used to sample from a larger population depends on the type of analysis being performed.

There are two methods of selecting from populations: non-random or judgment sampling, and random or probability sampling.
Random sampling is a probability sampling method that utilizes some form of random selection to assure equal probabilities of being chosen.

The sampling distribution is the distribution of all possible values of a statistic from all possible samples of a particular size drawn from the population.
Each sample drawn from a population would have its own means or measure of central tendency and standard deviation.

The standard deviation of the distribution of the sample means is called the standard error of the mean.
The standard error of the proportion is the standard deviation of the distribution of the sample proportions.
The standard error measures the extent to which the means vary due to chance error in the sampling process.