Mode:
The mode refers to the value that appears most frequently in a given dataset. A dataset may be:
- Unimodal, with one mode
- Bimodal, with two modes
- Multimodal, with more than two modes
- Without a mode, if all values occur with equal frequency
Example: In the dataset {2, 3, 3, 4, 5, 5, 5, 6}, the mode is 5, as it occurs three times—more than any other value.
Median and Quartiles:
The median represents the middle value that divides a dataset into two equal halves when the data is arranged in order.
Quartiles are values that divide the dataset into four equal parts:
- Q1 (First Quartile): Marks the 25th percentile
- Q2 (Second Quartile): Also known as the median (50th percentile)
- Q3 (Third Quartile): Marks the 75th percentile
These measures provide insight into the distribution and spread of the data.
Relationship Between Median, Quartiles, and Mode:
The median (Q2) is both a quartile and a measure of central tendency. While the mode does not directly correspond to the quartiles, it complements them by identifying the most frequently occurring value. When the mode differs significantly from the median, it may indicate a skewed distribution.
Use in Data Representation:
Datasets can be analyzed and compared using central tendency measures (such as the mean, median, and mode) as well as measures of dispersion (like quartiles and range). Tools such as box plots graphically display the median, quartiles, and overall data spread, allowing for easier visual comparison between datasets.
Quantiles and Quartiles:
Quantiles are statistical cut points that divide a dataset into equal-sized intervals. Quartiles are specific quantiles that divide the data into four equal parts. Thus, all quartiles are quantiles, but not all quantiles are quartiles. Quartiles serve as a fundamental tool in descriptive statistics for understanding data distribution.
