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COMPUTATIONAL REVIEW - Basic questions about statistics

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In this assignment, you will complete a Computational Review and answer basic questions about statistics. Complete the answers on the document. COMPUTATIONAL REVIEW Now that we have finished our basic introduction, how about doing some basic math review? This review is simply to lube your memory banks and get the gears moving without squeaking; nothing more, nothing less. Okay, here we go.Remember that a negative sign in front of the fraction conveys that either the numerator or the denominator is a negative number. However, both cannot be negative. Why, you say? Because a negative numbe...

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Question Preview:

In this assignment, you will complete a Computational Review and answer basic questions about statistics. Complete the answers on the document. COMPUTATIONAL REVIEW Now that we have finished our basic introduction, how about doing some basic math review? This review is simply to lube your memory banks and get the gears moving without squeaking; nothing more, nothing less. Okay, here we go.Remember that a negative sign in front of the fraction conveys that either the numerator or the denominator is a negative number. However, both cannot be negative. Why, you say? Because a negative number divided by another negative number would be a positive number. For example, (-1/2) (3/4) = -3/8 or -(1/2) (3/4) = -3/8. In this instance the negative sign could be either inside or outside the parentheses. To divide by a fraction, you simply invert the divisor and multiply. For example: ¾ ÷ ½ = 2/1 x ¾ = 6/4 = 1 ½. How about that? On the other hand, to multiply two fractions, simply multiply the numerators then multiply the denominators of each fraction. How about an example of 2/3 x 1/3? Well, 2/3 x 1/3 = 2 x 1/3 x 3 = 2/9. Simple isn’t it? Now to addition. The addition or subtraction of fractions involves a process of finding a common denominator, if the denominators are different. For example, ¼ + 2/9 have different denominators (4 and 9). So, we must find a denominator that would be common to both fractions. The smallest number that is common to both denominators (4 and 9) would be 36. Therefore, we would transform the problem to read: ¼ + 2/9 = 9/36 + 8/36 = 17/36 (4 into 36 = 9 and 9 x 1= 9 (9/36), while 9 into 36 = 4 and 4 x 2=8 (8/36). Now, how about subtracting some fractions? Okay, 3/7 – 2/9 = ? The common denominator here would be 63. Therefore, we would transform 3/7 – 2/9 to 27/63 – 14/63 (7 into 63 = 9 and 9x3 = 27, while 9 into 63 = 7 and 7x2 = 14). So, now we have 27/63 – 14/63 = 13/63. What a snap! Now, let us change gears a bit and move to whole numbers. When you multiply or divide numbers carrying the same sign, the answer would be positive. However, if you multiply or divide numbers of different signs (one number having a positive sign and the other number having a negative sign), the answer would be negative. How about them apples? For example, 20 ÷ 5 = 4; -20 ÷ (-5) = 4; -20 ÷ 5 = -4; 20 ÷ -5 = -4; 20 x 5 = 100; -20 x (-5) = 100; -20 x 5 = -100; and 20 x (-5) = -100. When you add numbers of the same sign, the sign carries to the answer. However, when you add numbers of different signs, the answer will be the difference of the numbers and the sign of the largest number will be carried to the answer. For example, 10 + 6 = 16; 10 + (-6) = 4; (-10) + 6 = -4; and (-10) + (-6) = -16. And finally, when you encounter multiplication, division, addition, or subtraction problems in parentheses, you must perform the mathematic procedure within the parentheses first before continuing the problem solving task. For example, 6 (2 + 4)= 6 x 6 = 36; (10 – 3)(4 + 1) = 7 x 5 = 35; 8 + (9 ÷ 3) – [(6 + 2)(3 + 1)] = 8 + 3 – [8 x 4] = 8 + 3 – 32 = 11 – 32 = -21. Oh, by the way, brackets [ ] imply the same thing as parentheses. Sorry about that. Now, how about a test of your skill? No you say? Well, give it a try anyway.

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The Greek symbol Σ  means sum or to sum a set of numbers following it. So, ΣX would simply mean to sum all values of the variable X.  Now, go ahead and do it

 

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