Applying fractal statistics to the components of the Dow Jones Industrial Average that belong to the industries of telecommunications and technology, this study established the indicators of fractal distribution and examines the fractal spectrum of each of the stocks selected. From the said fractal spectrum, the researchers identified segments that represent similar fractal dimensions. The findings of this study gave an overall picture of the entire volatility level within selected stocks for the purpose of dissecting the said volatility level into smaller segments. Scrutinizing the fluctuations within a volatility level will be helpful for short term investors in identifying the price levels appropriate to their risk appetite. It is clearly manifested by the results of the fractal segmentation.