Finding the mean score of three different averages?
In a city with three high schools, all the ninth graders took a Standardized Test, with these results: High School Mean score on test Number of ninth graders Glenwood 76 287 Central City 95 339 Lincoln High 73 171 The city's PR manager, who never took statistics, claimed the mean score of all ninth graders in the city was 81.3 . Of course, that is incorrect. What is the mean score for all ninth graders in the city? Round to one decimal place.
What is the only right triangle that has sides in arithmetic progression?
Suppose a right angled triangle has sides [math]a-d, a, a+d[/math], so that they form an arithmetic progression. If we assume that both [math]a[/math] and [math]d[/math] are positive, then [math]a+d[/math] is the longest side of the right angled triangle, and we have[math](a-d)^2+a^2=(a+d)^2[/math][math]a^2-2ad+d^2+a^2=a^2+2ad+d^2[/math][math]a^2-4ad=0[/math][math]a(a-4d)=0[/math]So either [math]a=0[/math] (which does not make sense) or [math]a=4d[/math]. When [math]a=4d[/math], the three sides of the right angled triangle are [math]3d[/math], [math]4d[/math] and [math]5d[/math] respectively.So the right-angled triangle whose sides are in an A.P. is the one whose sides are in the ratio [math]3:4:5[/math].
What is the infinite average between arithmetic mean and geometric mean of two positive numbers x and y?
The value described in the linked image is called the Arithmetic–geometric mean. The formula given (with proof) at that Wikipedia link says that[math]\text{agm}(x,y)=\dfrac\pi4\cdot \dfrac{x+y}{K\left(\frac{x-y}{x+y}\right)}\tag*{}[/math]where[math]K(t)=\displaystyle\int_0^{\pi/2}\frac{d\theta}{\sqrt{1-t^2\sin^2\theta}}\tag*{}[/math]So, for example,[math]\text{agm}(1,2)\doteq 1.45679[/math][math]\text{agm}(1,3)\doteq 1.86362[/math][math]\text{agm}(1,4)\doteq 2.24303[/math]What is the infinite average between arithmetic mean and geometric mean of two positive numbers x and y? Imgur: The magic of the Internet
What are the first 4th terms of an arithmetic sequence in which a1=x-y and d=3y?
The first four terms of the AP, whose first term is a1=x-y and d = 3y are(x-y), (x+2y), (x+5y) and (x+8y).
Three sections of a statistics class containing 28, 32, and 35 students averaged 83, 80, and 76 respectively. What is the average of all 3 sections?
For each section (for example the section with 28 students) the average (mean) is calculated by(sum of all 28 scores)/28 = 83Multiply both sides by 28 and we get: (sum of all 28 scores) = 83 x 28 = 2324For the section with 32 students: (sum of all 32 scores) = 80 x 32 = 2560For the section with 35 students: (sum of all 35 scores) = 76 x 35 = 2660So, the sum of scores for all 3 sections is 2324 + 2560 + 2660 = 7544This is the total of all scores for the 28 + 32 + 35 = 95 students.The average (mean) of all 95 students is(sum of all students)/(sum of all students) = 7544/95 = 79.4 to one decimal place
How does the geometric mean differ from the standard deviation?
The geometric mean (GM) is a measure of the central tendency whereby the standard deviation (SD) is a measure of dispersion.GM indicates the aggregation or typical value of a group of quantitative observations by using the product of their values (as opposed to the arithmetic mean which uses their sum). The geometric mean is defined as the nth root of the product of n numbers. That is, we multiply the numbers together and then take a square root (for two numbers), cube root (for three numbers) etc.GM applies only to numbers of the same sign. It is often used for numbers whose values are meant to be multiplied together or are exponential in nature, such as data on the growth of the human population or interest rates of a financial investment.SD measures the spread of a set of data from its mean. In addition to expressing the variability of a population, the SD is commonly used to calculate confidence intervals. In finance, SD is often used to measure the volatility or risk of instruments such as stocksHere’s the Wikipedia article about geometric means: Geometric mean - WikipediaHere’s the Wikipedia article about standard deviations: Standard deviation - Wikipedia
Why is the term geometric related to multiplication and the term arithmetic to addition?
Why is the term geometric related to multiplication and the term arithmetic to addition?This is a great question.The answer to this has to do with the nature of multiplication as scaling and gets right to the heart of the debates from awhile ago regarding the definition of multiplication taught in K-12 math classes.Google maps provides a good way to think about the relationship between addition and multiplication - translating a map horizontally or vertically involves addition, and zooming in or out is scaling and involves multiplication.Ask just about any high school student or math teacher whether or not multiplication is defined as repeated addition, and they are likely to say “Yes”.However, that is not true. Multiplication is not algebraically defined as repeated addition, and the teachers who insist that their Algebra students memorize and apply the field axioms invalidate their own understanding of what a field is if they assert that such a definition exists.Ask someone to explain what multiplication is, and they will usually use a repeated addition model. Seldom will they think of using geometric similarity as a model, but this is where the association comes from.Two figures that are similar to each other have corresponding parts in equivalent ratios. When one figure is twice as big as another, we don’t think in terms of ‘adding’ the original figure to itself to yield the other. Rather, we ‘stretch’ it.‘Arithmetic’ comes from Greek ‘arithmos’, number, and the use of the term usually has the sense of ‘counting’.Arithmetic arises from counting, and geometry arises from similarity.Also see my What does it mean to multiply (in mathematical and philosophical terms)?
What is the average mean value?
(In this the terms mean and average are interchangable)First define mean go to any math dictionary and try to decipher a definition, then we find the mean by adding all the numbers in the equations values together(3+5+1=9), then we divide the sum of the numbers by the amount of numbers in the equation(3+5+1=3)(remember i said amount of numbers not value), then divide to get the mean(9/3=3).Now that we have the mean we will find the average of the mean which is 3. So go to that same math dictionary and define average. Then we find the sum of all the numbers added together, which is 1, since theres only one 3, then we divide the sum of the numbers by the amount of number in the equation(3/1=3)I hope i explained this right i dont even know i the proof is right but i thought id give it a shot.