There is a common misconception that if total income is X then tax liability must be Y based on whatever tax bracket the total income falls into. In fact, it could not be further from the truth. In the U.S. we have what is called a "progressive" tax system. The first X of taxable income is subject to a tax rate of Y, then the next X of taxable income is subject to a tax rate of a different Y.
Let's look at an example. In 2014, single taxpayers are taxed at a rate of 10% on their first $9,075 of income. From $9,076 to $36,900 income is taxed at a rate of 15%. If a single taxpayer had total income of $35,150 they may assume that the tax liability is $35,150 * 15% = $5,272.50. However, in order to correctly calculate the tax liability we must first subtract the standard deduction of $6,200 and the personal exemption of $3,950, leaving them with taxable income of $25,000, which is over $10,000 less than the original $35,150. Then, we calculate the total tax liability based on $25,000 of taxable income:
For the first $9,075: 9,075 * 10% = $907.50
For the remainder: (25,000 - 9,076 = 15,924), 15,924 * 15% = $2,388.60
A total of: 2,388.60 + 907.50 = $3,296.10 tax liability
In our example, the single taxpayer's actual tax liability is $2,000 less than the tax liability they would have calculated by multiplying total income by the 15% tax bracket. The actual tax rate is just 9%.