Answers: 1) The first quartile (Q₁) = 11 ; 2) The median = 38.5 ; 3) The third quartile (Q₃) = 45 ; 4) The difference of the largest value and the median = 10.5 . _______ Explanation:
Given this data set with 8 (eight) values: → {6, 47, 49, 15, 43, 41, 7, 36}; →Rewrite the values in increasing order; to help us find the median, first quartile (Q,) and third quartile (Q₃) : → {6, 7, 15, 36, 41, 43, 47, 49}. →We want to find; or at least match; the following 4 (four) values [associated with the above data set] — 38.5, 11, 10, 45 ;
1) The first quartile (Q₁); 2) The median; 3) The third quartile (Q₃); & 4) The difference of the largest value and the median.
Note: Let us start by finding the "median". This will help us find the correct values for the descriptions in "Numbers 2 & 4" above. The "median" would be the middle number within a data set, when the values are placed in smallest to largest (or, largest to smallest). However, our data set contains an EVEN number [specifically, "8" (eight)] values. In these cases , we take the 2 (two) numbers closest to the middle, and find the "mean" of those 2 (two) numbers; and that value obtained is the median. So, in our case, the 2 (two) numbers closest to the middle are: "36 & 41". To get the "mean" of these 2 (two) numbers, we add them together to get the sum; and then, we divide that value by "2" (the number of values we are adding): → 36 + 41 = 77; → 77/2 = 38.5 ; → which is the median for our data set; and is a listed value. →Now, examine Description "(#4): The difference of the largest value and the median"—(SEE ABOVE) ; → We can calculate this value. We examine the values within our data set to find the largest value, "49". Our calculated "median" for our dataset, "38.5". So, to find the difference, we subtract: 49 − 38.5 = 10.5 ; which is a given value". →Now, we have 2 (two) remaining values, "11" & "45"; with only 2 (two) remaining "descriptions" to match; →So basically we know that "11" would have to be the "first quartile (Q₁)"; & that "45" would have to be the "third quartile (Q₃)". →Nonetheless, let us do the calculations anyway. →Let us start with the "first quartile"; The "first quartile", also denoted as Q₁, is the median of the LOWER half of the data set (not including the median value)—which means that about 25% of the numbers in the data set lie below Q₁; & that about 75% lie above Q₁.). →Given our data set: {6, 7, 15, 36, 41, 43, 47, 49}; We have a total of 8 (eight) values; an even number of values. The values in the LOWEST range would be: 6, 7, 15, 36. The values in the highest range would be: 41, 43, 47, 49. Our calculated median is: 38.5 . →To find Q₁, we find the median of the numbers in the lower range. Since the last number of the first 4 (four) numbers in the lower range is "36"; and since "36" is LESS THAN the [calculated] median of the data set, "38.5" ; we shall include "36" as one of the numbers in the "lower range" when finding the "median" to calculate Q₁ → So given the lower range of numbers in our data set: 6, 7, 15, 36 ; We don't have a given "median", since we have an EVEN NUMBER of values. In this case, we calculate the MEDIAN of these 4 (four) values, by finding the "mean" of the 2 (two) numbers closest to the middle, which are "7 & 15". To find the mean of "7 & 15" ; we add them together to get a sum; then we divide that sum by "2" (i.e. the number of values added up); → 7 + 15 = 22 ; → 22 ÷ 2 = 11 ; ↔ Q₁ = 11. Now, let us calculate the third quartile; also known as "Q₃". Q₃ is the median of the last half of the higher values in the set, not including the median itself. As explained above, we have a calculated median for our data set, of 38.5; since our data set contains an EVEN number of values. We now take the median of our higher set of values (which is Q₃). Since our higher set of values are an even number of values; we calculate the median of these 4 (four) values by taking the mean of the 2 (two) numbers closest to the center of the these 4 (four) values. This value is Q₃. →Given our higher set of values: 41, 43, 47, 49 ; → We calculate the "median" of these 4 (four) numbers; by taking the mean of the 2 (two) numbers in the middle; "43 & 47". → Method 1): List the integers from "43 to 47" ; → 43, 44, 45, 46, 47; → Since this is an ODD number of integers in sequential order; → "45" is not only the "median"; but also the "mean" of (43 & 47); thus, 45 = Q₃; → Method 2): Our higher set of values: 41, 43, 47, 49 ; → We calculate the "median" of these 4 (four) numbers; by taking the "mean" of the 2 (two) numbers in the middle; "43 & 47"; We don't have a given "median", since we have an EVEN NUMBER of values. In this case, we calculate the MEDIAN of these 4 (four) values, by finding the mean of the 2 (two) numbers closest to the middle, which are "43 & 47." To find the mean of "43 & 47"; we add them together to get a sum; then we divide that sum by "2" (i.e. the number of values added); → 43 + 47 = 90 ; → 90 ÷ 2 = 45 ; → 45 = Q₃ .
B. Tracing a sequence of events resulting in a positive outcome
Explanation:
Answer B
Correct. Writers frequently use certain recognizable approaches to develop and organize the reasoning of their arguments. In the opening lines of the passage, the author employs such a method of development when he traces a sequence of events that he believes have culminated in a positive outcome: the First World War happened; the war provided a cautionary example; world leaders have been trying to prevent another outbreak of war; in the end, they succeed in devising the “greatest preventive measures ever adopted by nations.” A method of development provides an audience with the means to trace a writer’s reasoning in an argument. In this case, the author’s approach to organizing his argument suggests that he understands recent peace preservation efforts in terms of a temporal chain of events—one in which each event is linked to the next by a causal logic.
Explanation: The placebo effect is defined as a phenomenon in which some people experience a benefit after the administration of an inactive substance or sham treatment. What exactly is a placebo? A placebo is a substance with no known medical effects, such as sterile water, saline solution, or a sugar pill.
The given angles sum to less than 90°, so the remaining angle must be more than 90°. (The total of all angles is 180°.) Triangle ABC has an angle greater than 90°, so is obtuse. Since the triangles are similar, their corresponding angles are congruent. Hence ...
