Statistics: Grouped Frequency Distribution

Grouped Frequency Distribution Table

• GFDT stands for Grouped Frequency Distribution Table, a method of presenting data in intervals.

Range

• The range is calculated by subtracting the minimum data value from the maximum data value.

Class Width

• Class width is determined by dividing the range by the number of groups, representing the span from the beginning to the end of a class.

Class Limits

• Class limits include lower and upper values defining the smallest and largest data points that can fit within a class, accurate to the data precision.

Class Boundary

• Class boundaries are positioned halfway between consecutive class limits, providing a more precise value with one additional degree of accuracy than the actual data limits.

Class Midpoint

• The class midpoint represents the average of the lower and upper class limits, serving as a central value for the class.

'Nice' Class Width

• A 'nice' class width is typically a multiple of 5 or 10, facilitating easier data interpretation and organization.

Histogram

• A histogram visually represents a GFDT as a bar graph where bars are adjacent, employing class boundaries for accurate data grouping.

Bell-Shaped Distribution

• Describes a disturbance with a central peak that symmetrically tapers off on both sides, often representing normal distribution.

Uniform Distribution

• A uniform distribution appears nearly flat, indicating similar frequencies across all classes.

J-Shaped Distribution

• Characterized by a disturbance that shows an increase in frequencies from left to right.

Reverse J-Shaped Distribution

• Reflects a disturbance where frequencies decrease from left to right.

Right-Skewed Distribution

• A right-skewed disturbance resembles a bell curve when the right side is obscured, with a longer tail on the right.

Left-Skewed Distribution

• A left-skewed disturbance shows a bell curve when the left side is hidden, featuring a longer tail on the left.

Bimodal Distribution

• A bimodal distribution has two distinct peaks, indicating two prevalent groups within the data.

U-Shaped Distribution

• This disturbance peaks on both ends, while the center dips down, forming a U-like shape.

Frequency Polygon

• A frequency polygon displays data via dots connected by lines at class midpoints, anchoring to the x-axis before and after the dataset.

Time Series Graph

• Utilizes dots and lines to represent data over time, plotting time on the x-axis without anchoring.

Quartiles

• Quartiles are unique percentiles that signify the location of data within a dataset, dividing the data into four equal parts.

First Quartile

• The first quartile corresponds to the 25th percentile, marking a quarter of the dataset below this value.

Second Quartile (Median)

• The second quartile equates to the 50th percentile and often represents the dataset's median value.

Third Quartile

• The third quartile is aligned with the 75th percentile, indicating three-quarters of the data fall below this value.

Inner Quartile Range

• Calculated as Quartile 1 minus Quartile 3, providing insight into the spread of the middle 50% of the data.

Five Number Summary

• Comprises Minimum, Quartile 1, Median, Quartile 3, and Maximum values, summarizing key characteristics of the dataset.

Box Plots

• Box plots graphically depict the five-number summary, visually representing the distribution and spread of data through quartiles and extremes.