Semi-Quartile Range in Normal Symmetrical Distribution

In a normal symmetrical distribution, the semi-quartile range is one-fourth of the range. Let us understand this concept in detail.

Definition of Semi-Quartile Range

Semi-quartile range is a measure of variability or dispersion in a dataset. It is calculated as half of the difference between the first quartile (Q1) and the third quartile (Q3). Mathematically, semi-quartile range can be expressed as:

Semi-Quartile Range = (Q3 - Q1)/2

Definition of Range

Range is a simple measure of variability that represents the difference between the maximum and minimum values in a dataset.

Mathematically, range can be expressed as:

Range = Maximum value - Minimum value

Relation between Semi-Quartile Range and Range

In a normal symmetrical distribution, the semi-quartile range is one-fourth of the range. This is because the range is the difference between the maximum and minimum values, while the semi-quartile range is the difference between the first and third quartiles. In a normal symmetrical distribution, the distance between the median and the quartiles is one-fourth of the distance between the median and the extreme values. Therefore, the semi-quartile range is one-fourth of the range.

Conclusion

Hence, we can conclude that in a normal symmetrical distribution, the semi-quartile range is one-fourth of the range. This relationship helps to understand the spread of data in a dataset.