values less than 5 are rounded down, meaning the previous digit remains the same; 0.54 becomes 0.5. If the last digit is exactly 5, whether or not you round depends on the preceding digit. If the preceding digit is odd, round up by adding one to it; if the preceding digit is even, leave it unchanged. For example, 32.635 rounds to 32.64, but 32.645 also rounds to 32.64.Always remember the order of operations in math. These are work in (1) parentheses, (2) exponents and square roots, (3) multiplication, (4) division, and (5) addition and subtraction. The acronym PEMDAS can help you to remember this order.Finally, remember that you may need to reorder an equation to solve for an unknown value. Remember the basic rules of algebra, which state that what is done to one side of an equation (equals sign) must be done to the other. For example, if 12 = 4X + 4, subtracting 4 from both sides give you 12 − 4 = 4X. Both sides can then be divided by 4, which provides the answer of X = 2.
Σ(X) is the symbol for summation. It indicates that you should sum all of the values of X.
Computational Exercises
1 (4)(5) + 3 =
2
3
4 Round your answer to two decimal places:
5 Round the following numbers to two decimal places:a. 6.8236; b. 3.4623; c. 5.2181
6 What is the reciprocal of the following?a. 4; b. 3; c. 2; d. 2/3
7 Complete the following chart:
8 Solve the following equations, remembering the rules of the order of operations:(12 + 45) − (54 − 9) =(4 + 3)2 − (20 − 7) =
9 Solve for X in the following equations:a. X + 3 = 10 b. 6X − 8 = 22 c. X − (2 + 6)2 = 36
10 Solve for X in the following equations:aX + b = c
11 Expand and solve the following expressions if X1 = 2; X2 = 4; X3 = 9:ΣX =(ΣX)2 =ΣX 2 =Σ2X =2ΣX =
12 12. Expand the following binomials:2(a + b) =(a + b)2 =3(a + b)2 =
Computational Answers
1 23
2 9
3 5
4 16.5
5 a. 6.82; b. 3.46; c. 5.22
6 a. 1/4; b. 1/3; c. 1/2; d. 3/2
7 Complete the following chart:
8 Solve the following equations, remembering the rules of the order of operations:a. 12; b. 19; c. 8; d. 36; e. 13
9 Solve for X in the following equations:a. X = 7; b. X = 5; c. X = 100
10 Solve for X in the following equations:
11 Expand and solve the following expressions if X1 = 2; X2 = 4; X3 = 9:a. 15; b. 225; c. 101; d. 30; e. 30
12 Expand the following binomials:a. 2a + 2b; b. a2 + 2ab + b2; c. 3a2 + 6ab + 3b2
True/False Questions
1 Statistics are used to summarize populations, whereas parameters are used to summarize samples.
2 Both X-bar () and M are symbols for means.
3 p and q are related in that as one increases the other decreases.
4 The absolute value of −8 is −8.
5 In doing a complicated math problem, you should complete work in parentheses first.
6 6.42338139 rounded to two decimal places is 6.42.
7 Σ(X + Y) is the same as ΣX + ΣY.
True/False Answers
1 False
2 True
3 True
4 False
5 True
6 True
7 True
Short-Answer Questions
1 Describe how a sample and a population differ and how they are related.
2 What is precision in mathematical calculation? How precise should you be when working on a question in statistics? When stating your answer?
3 What is the correct order in which mathematical operations must be conducted?
4 What, if any, is the difference between a case and a subject or participant?
Answers
1 Samples are small subgroups of populations. Populations consist of larger groups that contain all of the individuals in your area of interest. They are related in that samples are derived from populations and are used to infer about populations.
2 Precision is the exactness of the calculation, or how many decimal places are used. In social science statistics, we generally use three decimal places when working through a problem and present the final answer rounded to two decimal places.
3 Calculations within parentheses, exponents, multiplication, division, addition, and subtraction.
4 A case represents an individual unit of study. A subject or participant represents an individual human being in a study.
Multiple-Choice Questions
1 If p = .45, then q =.45.65.551
2 The average person drinks approximately 8 glasses of water per day, what is the appropriate symbol to represent this measurement?NnMX
3 What is another way to express 1/4?.745%.925%
4 What is another way to express ≈.33?4/72/665%46%
5 According to the conventions of the social sciences, what is the solution: 4.541 + 6.327?10.86810.8710.910
6 What is another method to express Σ(3X + 4Y)?(12)Σ(X + Y)2Σ(3X) + Σ(4Y)3+Σ(X) + 4 + Σ(Y)Σ(3X)2 + Σ(4Y)2
7 Solve for Z: Z = 20Z = 3.75Z = 4.25Z = 10.50
8 Solve for X: 20X − 18 = 6(X + 4)X = 4X = 5.5X = 12X = 3
Multiple-Choice Answers
1 C
2 C
3 D
4 B
5 B
6 B
