
Concept explainers
Find (a) the mean, (b) the median, (c) the mode, and (d) the standard derivation of the following set of the raw material.

(a)
To find:
The mean of the following set of raw material.
Answer to Problem 1CR
Solution:
The mean of the given set of raw material is
Explanation of Solution
Given:
The given following set of raw material is,
Formula used:
The mean is the ratio of the sum of the data points to the number of the data points.
Consider the mean formula,
Here, the mean is
Calculation:
Consider the given set of raw materials,
Consider the total sum of the raw materials,
Consider the total number of data points,
Consider the mean formula,
Substitute
Thus, the mean of the given set of raw material is
Conclusion:
Thus, the mean of the given set of raw material is

(b)
To find:
The median of the following set of raw material.
Answer to Problem 1CR
Solution:
The median of the given data is
Explanation of Solution
Given:
The given following set of raw material is,
Formula used:
The median is the middle value of a distribution of numbers.
Consider the median position formula,
Here, the median number position is
Consider the median number formula,
Here, the median number is
Calculation:
Consider the given set of raw materials,
Consider the total number of data points,
Consider the mean formula,
Substitute
Thus, the median of the given set of raw material is
Consider the fifth raw material,
Consider the sixth raw material,
Consider the median number formula,
Substitute
Thus, the median of the given data is
Conclusion:
Thus, the median of the given data is

(c)
To find:
The mode of the following set of raw material.
Answer to Problem 1CR
Solution:
The mode of the given set of raw material is
Explanation of Solution
Given:
The given following set of raw material is,
Concept:
The mode is the data points with highest frequency. Because it represents the most common number, the mode can be viewed as an average.
Approach:
Consider the given set of raw materials,
The frequency of the number
The frequency of the number
The frequency of the number
The frequency of the number
The frequency of the number
The frequency of the number
Therefore, the mode is
Thus, the mode of the given set of raw material is
Conclusion:
Thus, the mode of the given set of raw material is

(d)
To find:
The standard derivation of the following set of raw material.
Answer to Problem 1CR
Solution:
The standard derivation of the given set of raw material is
Explanation of Solution
Given:
The given following set of raw material is,
Formula used:
The mean is the ratio of the sum of the data points to the number of the data points.
The variance of the sample is found by dividing the sum of squares of the deviations by
The square root of the variance is called standard variance.
Consider the mean formula,
Here, the mean is
Consider the variance formula,
Here, the variance is
Consider the standard formula,
Here, the standard deviation is
Calculation:
Consider the given set of raw materials,
Consider the total sum of the raw,
Consider the total number of data points,
Consider the mean formula,
Substitute
Thus, the mean of the given set of raw material is
Consider sum of squares of the deviations,
Consider the variance formula,
Substitute
Therefore, the variance is
Consider the standard formula,
Substitute
Thus, the standard deviation is
Conclusion:
Thus, the standard deviation is
Want to see more full solutions like this?
Chapter 4 Solutions
Mathematics: A Practical Odyssey
- 8arrow_forward74. Geometry of implicit differentiation Suppose x and y are related 0. Interpret the solution of this equa- by the equation F(x, y) = tion as the set of points (x, y) that lie on the intersection of the F(x, y) with the xy-plane (z = 0). surface Z = a. Make a sketch of a surface and its intersection with the xy-plane. Give a geometric interpretation of the result that dy dx = Fx F χ y b. Explain geometrically what happens at points where F = 0. yarrow_forwardExample 3.2. Solve the following boundary value problem by ADM (Adomian decomposition) method with the boundary conditions მი მი z- = 2x²+3 дг Əz w(x, 0) = x² - 3x, θω (x, 0) = i(2x+3). ayarrow_forward
- 6. A particle moves according to a law of motion s(t) = t3-12t2 + 36t, where t is measured in seconds and s is in feet. (a) What is the velocity at time t? (b) What is the velocity after 3 s? (c) When is the particle at rest? (d) When is the particle moving in the positive direction? (e) What is the acceleration at time t? (f) What is the acceleration after 3 s?arrow_forwardpls help asaparrow_forwardQ1.4 1 Point V=C(R), the vector space of all real-valued continuous functions whose domain is the set R of all real numbers, and H is the subset of C(R) consisting of all of the constant functions. (e.g. the function ƒ : R → R defined by the formula f(x) = 3 for all x E R is an example of one element of H.) OH is a subspace of V. H is not a subspace of V. Save Answerarrow_forward
- Solve the following LP problem using the Extreme Point Theorem: Subject to: Maximize Z-6+4y 2+y≤8 2x + y ≤10 2,y20 Solve it using the graphical method. Guidelines for preparation for the teacher's questions: Understand the basics of Linear Programming (LP) 1. Know how to formulate an LP model. 2. Be able to identify decision variables, objective functions, and constraints. Be comfortable with graphical solutions 3. Know how to plot feasible regions and find extreme points. 4. Understand how constraints affect the solution space. Understand the Extreme Point Theorem 5. Know why solutions always occur at extreme points. 6. Be able to explain how optimization changes with different constraints. Think about real-world implications 7. Consider how removing or modifying constraints affects the solution. 8. Be prepared to explain why LP problems are used in business, economics, and operations research.arrow_forwardConstruct a table and find the indicated limit. √√x+2 If h(x) = then find lim h(x). X-8 X-8 Complete the table below. X 7.9 h(x) 7.99 7.999 8.001 8.01 8.1 (Type integers or decimals rounded to four decimal places as needed.)arrow_forwardExample 3.2. Solve the following boundary value problem by ADM (Adomian decomposition) method with the boundary conditions მი მი z- = 2x²+3 дг Əz w(x, 0) = x² - 3x, θω (x, 0) = i(2x+3). ayarrow_forward
- Use the graph to find the following limits. (a) lim f(x) (b) lim f(x) X-1 x→1 (a) Find lim f(x) or state that it does not exist. Select the correct choice X-1 below and, if necessary, fill in the answer box within your choice. OA. lim f(x) = X-1 (Round to the nearest integer as needed.) OB. The limit does not exist. Qarrow_forwardOfficials in a certain region tend to raise the sales tax in years in which the state faces a budget deficit and then cut the tax when the state has a surplus. The graph shows the region's sales tax in recent years. Let T(x) represent the sales tax per dollar spent in year x. Find the desired limits and values, if they exist. Note that '01 represents 2001. Complete parts (a) through (e). Tax (in cents) T(X)4 8.5 8- OA. lim T(x)= cent(s) X-2007 (Type an integer or a decimal.) OB. The limit does not exist and is neither ∞ nor - ∞. Garrow_forwardDecide from the graph whether each limit exists. If a limit exists, estimate its value. (a) lim F(x) X➡-7 (b) lim F(x) X-2 (a) What is the value of the limit? Select the correct choice below and, if necessary, fill in the answer box within your choice. OA. lim F(x) = X-7 (Round to the nearest integer as needed.) OB. The limit does not exist. 17 Garrow_forward
- Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw HillBig Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin HarcourtHolt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGAL



