7: Operations on Numbers
This chapter is from the Support Course for Elementary Statistics by Larry Green from Lake Tahoe Community College.
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- 7.2: Factorials and Combination Notation
- When we need to compute probabilities, we often need to multiple descending numbers. For example, if there is a deck of 52 cards and we want to pick five of them without replacement, then there are 52 choices for the first pick, 51 choices for the second pick since one card has already been picked, 50 choices for the third, 49 choices for the fourth, and 48 for the fifth.
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- 7.3: Order of Operations
- When we are given multiple arithmetic operations within a calculation, there is a, established order that we must do them in based on how the expression is written. Understanding these rules is especially important when using a calculator, since calculators are programmed to strictly follow the order of operations. This comes up in every topic in statistics, so knowing the order of operations is an essential skill for all successful statistics students to have.
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- 7.4: Order of Operations in Expressions and Formulas
- We have already encountered the order of operations: Parentheses, Exponents, Multiplication and Division, Addition and Subtraction. In this sections we will give some additional examples where order of operations must be used properly to evaluate statistics.
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- 7.5: Perform Signed Number Arithmetic
- Even though negative numbers seem not that common in the real world, they do come up often when doing comparisons. For example, a common question is how much bigger is one number than another, which involves subtraction. In statistics we don't know the means until we collect the data and do the calculations. This often results in subtracting a larger number from a smaller number which yields a negative number. We need to be able to perform arithmetic on both positive and negative numbers.
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- 7.6: Powers and Roots
- It can be a challenge when we first try to use technology to raise a number to a power or take a square root of a number. In this section, we will go over some pointers on how to successfully take powers and roots of a number. We will also continue our practice with the order of operations, remembering that as long as there are no parentheses, exponents always come before all other operations. We will see that taking a power of a number comes up in probability.
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- 7.8: Solving Equations Using the Subtraction and Addition Properties of Equality
- To determine whether a number is a solution to an equation, first substitute the number for the variable in the equation. Then simplify the expressions on both sides of the equation and determine whether the resulting equation is true. If it is true, the number is a solution. If it is not true, the number is not a solution. The Subtraction and Addition Properties of Equality help in solving for the variable in an equation.
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- 7.9: Introduction to Inequalities and Interval Notation
- An algebraic inequality, such as 𝑥≥2 , is read “ 𝑥 is greater than or equal to 2 .” This inequality has infinitely many solutions for 𝑥 . Some of the solutions are 2,3,3.5,5,20, and 20.001 . Since it is impossible to list all of the solutions, a system is needed that allows a clear communication of this infinite set. Two common ways of expressing solutions to an inequality are by graphing them on a number line and using interval notation.
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- 7.10: Translating English to Math
- When working with probability and statistics, words such as “more than” or “less than” can drastically change the answer. It is important to be able to translate to math some of the common phrases you may run into while reading a problem. It will be essential later in the course that you can correctly match these phrases with their correct symbol.