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 .
This is just a mathematics question but factoring is use a lot of times to make numbers smaller and easier to work with that is in the case of GCF 14(x^2 + y^3) you would multiply it out but it is easier to work with
Answer:Astronomers estimate the age of the universe in two ways: 1) by looking for the oldest stars; and 2) by measuring the rate of expansion of the universe and extrapolating back to the Big Bang; just as crime detectives can trace the origin of a bullet from the holes in a wall.
1. The short-run equilibrium price level and output are PL² and Y¹, where Equilibrium Price is PL₂ and Equilibrium Output is Y¹.
<h3>What is Fiscal Policy?</h3>
Fiscal policy is defined as the use of government spending and tax policies to regulate and control the economic situation of a country. The conditions controlled in this case are macro-economic indices such as inflation, unemployment, equilibrium wage levels, etc.
2. If the Short-Run Equilibrium price level falls, the new equilibrium price level will become PL¹. This is because the next lowest price level below PL² is PL¹.
3. If Investment (or spending or demand) is increased in the short run, the equilibrium price level will sit at PL³.
4. After a negative supply shock (that is supplies took a negative turn), the new short-run equilibrium price will be fixed at PL¹ with Y being equal to Y¹.
5. If the real GDP was Y³ the type of Unemployment that could result are:
Demand Deficient Unemployment and
Voluntary Unemployment.
Demand Deficient Unemployment occurs because the company no longer has sufficient demand for its products to sustain its operations. This leads to the company reducing production as well as its workforce. Notice the huge huge unmet demand as depicted in points PL²Y², PL³Y³, and PL₁Y¹ (See attached image for the shaded region).
Voluntary Unemployment is similar to demand deficient Unemployment. The causes are the same. The difference here is that the employees voluntarily resign because it is no longer financially rewarding. This may be due to huge pay reductions as a result of low demand oversupply.
6. Where the GDP or output was Y², the type of unemployment that would exist is called Natural unemployment. Note that Y² is the equilibrium output point. Natural unemployment is the difference between those who want to do a job at the present wage rate and those who do not want to due to personal choices or the ability to do so.
7. The long-run equilibrium price (LRAS) where the ages and resources are flexible will be PL¹, PL², PL³, and PL⁴. This is because, in the long run, the economy can create natural levels of employment and potential output at any given price level.
8. Based on the question and the information provided by the graph, the long-run equilibrium output will stand at Y⁴ if government spending increases.