MAT 2379 Lecture Notes - Lecture 13: Quartile, Box Plot, Interquartile Range

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1 Nov 2016

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In descriptive statistics, we understand how to find the sample mean, standard deviation, variance, median of a variable. The average of all calculation is called the sample mean, this can be found by adding all the x values observed and dividing it by n (the number of observed values) For example, if the weight of 5 people is measured to be 53. 1, 56. 4, 90, 80, 49 then the sample mean or average weight of the population is the sum of 53. 1, 56. 4, 90, 80, 49 divided by 5. The deviation is the difference between a data point and its mean. The sum of the deviation has to be zero. To calculate the sample mean using r, input the values and then type mean(x) The sample median is the value of x observed that divides all the values of x arranged in increasing order to half. Arranging the values in increasing order is called order statistics.

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Help with 38,42,47,55 please

Mnct 60. fx)-3x3x 61, f(x) = x.(x-z? Applications of Differentiation 212 CHAPTER 3 Find all critial hunber 35. 40, g(Î¸)-48-tane 39. F(x)-x""(x-4): 41. f)-2 cos8 + sino 63. Between 0Â°C and 30Â°C, the volume V Gn of I kg of water at a temperature T is 43-44 A formala for the derivartive of a function f'is given. How many critical numbers does f have? V-999.87-0.06426T0.00850437 Find the temperature at which water has its m APTE - 6x + 10 64. An object with weight W is dragged along a h attached to the o by a force acting along a rope rope makes an angle Î¸ with the plane, then the 45-56 Find the absolute maximum and absolute minimurn values the force is Î¼ sin Î¸ + cos Î¸ of f on the given interval. 45. fx)-12+4x -. [0,S] 46. fix)-5+54x-2x. (0,4) å¸f(x)-2x,-3x1-12x + 1, [-23] where Î¼ is a positive constant called the coefficie and where 0 Î¸ Ï/2. Show that F is minimize 65. The water level, measured in feet above mean sea l Lake Lanier in Georgia, USA, during 2012 can be im the function L()-0.01441,, 50. f)- 4). [-2,3] 51.)(02.4) 52. x)-+T -0.4177,2 + 2703t + 1060. where t is measured in months since January 1,201 when the water level was highest during 2012. 66. On May 7, 1992, the space shuttle Endeavour was laun on mission STS 49, the purpose of which was to install perigee kick motor in an Intelsat communications satellit The table gives the velocity data for the shuttle between l and the jettisoning of the solid rocket boosters. (a) Use a graphing calculator or computer to find the cubi S4. ft)- 0.2 pol ymomial that best models the velocity of the shuttle interval r e [o, 125). Then graph this polynom acceleration of the shuttle and usew ss fc)-2 cos+sin 2t, [o, -/2 56. f(t)-' + cot('/2), [Ï/4.7v/4] 57. If a and b are positive bumbers, find the maximum value 58. Use a graph ximum and minimum values of the to estimate the critical numbers of fx)-II+5xcorect i e decil place 59-62 (a) Use a graph to estimate the absolute (b) Use calculus to find the exact 0 maximurm and 0 185 319 447 values of the function to two decimal places. minimum maxirsum and minimum values 20 32

General Math Terms A product B. digit C. numeral D. compass E. equation F. formula G. negative H. sum I. mean J. statistics K. positive L. percent M. straight-edge N. squareroot O. quotient P. prime numbers Q. difference R. addend S. minuend T. divisor Greater than zero: plus. A number being added to another number. A mathematical sequence whose verb is equal (=). The result of addition. The number doing the dividing in a division problem. An instrument used to construct straight lines. A mathematical expression of a natural law. The result of multiplication. The number from which another number is being subtracted. Any non-negative numeral less than ten. Less than zero: minus. An instrument used to construct circles and arcs of circles. A number that produces another number (it's square) when multiplied by itself. The result of subtraction. A symbol or name of a number. The average: the sum of the elements divided by the number of elements. The result of division. Parts per hundred: hundredths. Natural numbers greater than one that have no other factors except one and themselves. Set of numerical data. Geometry A. chord B. diameter C. radius D. perimeter E. cylinder F. surface area G. right angle H. square I. Hypotenuse J. obtuse angle K. vertex L point M. ray N. bisect O arc P. hexagon Q. pentagon R. polygon S. perpendicular T. rectangle U. rhombus V. triangle W. circumference X cube Y pyramid Z. sphere A six-sided polygon. The common end point of the sides of an angle. An angle measuring more than 90 degree. A long, round object with flat, circular ends. An angle of 90 degree. The side of a right triangle opposite the right angle. The total area of all the surfaces of an object. To multiply a number by itself. A location, the place where two lines cross or intersect. A closed geometric figure made up of three or more line segments. The perimeter of a circle: the distance around a circle. A shape having the same dimensions of length, height, and width. A half-line with a designated end point which extends in only one direction without stopping. A figure having a polygon base and triangular sides which meet in a point at the top. Divide an angle into two equal angles. A part of a circle

Q1. Determine, without graphing, whether the quadratic function f(x) = x2 + 2x - 6 has a maximum value or a minimum value and then find that value. a. minimum; -7 b. minimum; -1 c. maximum; -1 d. maximum; -7 Q2. Find (f - g)(4) when f(x) = 5x2 + 6 and g(x) = x + 2. a. 80 b. 88 c. 84 d. -90 Q3. The graph of a function is given. Decide whether it is even, odd, or neither. a. even b. odd c. neither Q4. Find the average rate of change for the function f(x) = -3x2 - x from the values 5 to 6. a. 1/2 b. -2 c. -34 d. -1/6 Q5. Find the vertex and axis of symmetry of the graph of the function f(x) = 3x2 + 36x. a. (-6, -108); x = -6 b. (-6, 0); x = -6 c. (6, -108); x =6 d. (6, 0); x = 6 Q6. The graph of a function is given. Decide whether it is even, odd, or neither. a. even b. odd c. neither Q7. Use the graph to find the intervals on which it is increasing, decreasing, or constant. a. Increasing on (-3, -2) and (2, 4); decreasing on (-1, 1); constant on (-2, -1) and (1, 2) b. Decreasing on (-3, -2) and (2, 4); increasing on (-1, 1); constant on (-2, -1) and (1, 2) c. Decreasing on (-3, -2) and (2, 4); increasing on (-1, 1) d. Decreasing on (-3, -1) and (1, 4); increasing on (-2, 1) Q8. Graph the function F(x) = -5. State whether it is increasing, decreasing, or constant. a. b. c. d. Q9. Determine algebraically whether f(x) = -2x3 is even, odd, or neither. a. even b. odd c. neither Q10. Find the average rate of change for the function f(x) = 3/(x - 2) from the values 4 to 7. a. 7 b. 1/3 c. -3/10 d. 2 Q11. For the graph of the function y = f(x), find the absolute maximum and the absolute minimum, if it exists. a. Absolute maximum: f(4) = 7; Absolute minimum: f(1) = 2 b. Absolute maximum: f(4) = 7; Absolute minimum: none c. Absolute maximum: none; Absolute minimum: none d. Absolute maximum: none; Absolute minimum: f(1) = 2 Q12. The graph of a function f is given. Find the numbers, if any, at which f has a local minimum. What are the local minima? a. f has a local minimum at x = -2; the local minimum is 0 b. f has a local minimum at x = 0; the local minimum is 3 c. f has a local minimum at x = -2 and 2; the local minimum is 0 d. f has no local minimum Q13. Graph the function h(x) = -2x + 3. State whether it is increasing, decreasing, or constant. a. b. c. d. Q14. Find -f(x) when f(x) = -2x2 + 5x + 2. a. 2x2 - 5x + 2 b. -2x2 - 5x - 2 c. -2x2 - 5x + 2 d. 2x2 - 5x - 2 Q15. Determine algebraically whether f(x) = 1/x2 is even, odd, or neither. a. even b. odd c. neither Q16. Match the graph to one of the listed functions. a. f(x) = x2 - 8 b. f(x) = -x2 - 8x c. f(x) = x2 - 8x d. f(x) = -x2 - 8 Q17. In a certain city, the cost of a taxi ride is computed as follows: There is a fixed charge of $2.90 as soon as you get in the taxi, to which a charge of $1.70 per mile is added. Find an equation that can be used to determine the cost, C(x), of an x-mile taxi ride. a. C(x) = 1.70 + 2.90x b. C(x) = 3.10x c. C(x) = 4.60x d. C(x) = 2.90 + 1.70x Q18. Graph the function f(x) = -x2 + 3 by starting with the graph of y = x2 and using transformations (shifting, compressing, stretching, and/or reflection). a. b. c. d. Q19. Graph the function f(x) = x2 + 8x + 7 using its vertex, axis of symmetry, and intercepts. a. b. c. d. Q20. Determine where the function f(x) = -x2 + 8x - 7 is increasing and where it is decreasing. a. increasing on (4, â) and decreasing on (-â, 4) b. increasing on (-â, 4) and decreasing on (4, â) c. increasing on (9, â) and decreasing on (-â, 9) d. increasing on (-â, 9) and decreasing on (9, â) Q21. Find the domain of the rational function f(x) = (x + 9)/(x2 - 4x). a. {x|x â -2, x â 2} b. {x|x â -2, x â 2, x â -9} c. all real numbers d. {x|x â 0, x â 4} Q22. For the polynomial f(x) = 4(x - 5)(x - 6)3, list each real zero and its multiplicity. Determine whether the graph crosses or touches the x-axis at each x-intercept. a. 5, multiplicity 1, touches x-axis; 6, multiplicity 3 b. -5, multiplicity 1, touches x-axis; -6, multiplicity 3 c. 5, multiplicity 1, crosses x-axis; 6, multiplicity 3, crosses x-axis d. -5, multiplicity 1, crosses x-axis; -6, multiplicity 3, crosses x-axis Q23. Find all zeros of the function f(x) = 2x4 + 3x3 + 16x2 + 27x - 18 and write the polynomial as a product of linear factors. a. f(x) = (2x - 1)(x + 2)(x + 3)(x - 3) b. f(x) = (2x + 1)(x - 2)(x + 3)(x - 3) c. f(x) = (2x - 1)(x + 2)(x + 3i)(x - 3i) d. f(x) = (2x + 1)(x - 2)(x + 3i)(x - 3i) Q24. For the polynomial f(x) = (1/5)x(x2 - 5), list each real zero and its multiplicity. Determine whether the graph crosses or touches the x-axis at each x-intercept. a. 0, multiplicity 1, touches x-axis; â5, multiplicity 1, touches x-axis; -â5, multiplicity 1, touches x-axis b. 0, multiplicity 1, crosses x-axis; â5, multiplicity 1, crosses x-axis; -â5, multiplicity 1, crosses x-axis c. â5, multiplicity 1, touches x-axis; -â5, multiplicity 1, touches x-axis d. 0, multiplicity 1 Q25. List the potential rational zeros of the polynomial function f(x) = x5 - 6x2 + 5x + 15. Do not find the zeros. a. Â± 1, Â± 1/5, Â± 1/3 Â± 1/15 b. Â± 1, Â± 5, Â± 3, Â± 15 c. Â± 1, Â± 5, Â± 3 d. Â± 1, Â± 1/5, Â± 1/3, Â± 1/15, Â± 5, Â± 3,Â± 15 Q26. The function f(x) = x4 - 5x2 - 36 has the zero -2i. Find the remaining zeros of the function. a. 2i, 6, -6 b. 2i, 3i, -3i c. 2i, 3, -3 d. 2i, 6i, -6i Q27. Use transformations of the graph of y = x4 to graph the function f(x) = 5x4. a. b. c. d. Q28. State whether the function f(x) = x(x - 9) is a polynomial function or not. If it is, give its degree. If it is not, tell why not. a. Yes; degree 2 b. No; it is a product c. Yes; degree 0 d. Yes; degree 1 Q29. Solve the inequality algebraically. Express the solution in interval notation. (x - 2)2(x + 9) < 0 a. (-â, -9) or (9, â) b. (-â, -9] c. (-â, -9) d. (-9, â) Q30. Use the Intermediate Value Theorem to determine whether the polynomial function f(x) = -4x4 - 9x2 + 4; has a zero in the interval [-1, 0]. a. f(-1) = -9 and f(0) = -4; no b. f(-1) = 9 and f(0) = 5; no c. f(-1) = 9 and f(0) = -4; yes d. f(-1) = -9 and f(0) = 4; yes Q31. Use the Factor Theorem to determine whether x + 5 is a factor of f(x) = 3x3 + 13x2 - 9x + 5. a. Yes b. No Q32. Find a bound on the real zeros of the polynomial function f(x) = x4 - 8x2 - 9. a. -17 and 17 b. -9 and 9 c. -18 and 18 d. -10 and 10 Q33. Find the x-intercepts of the graph of the function f(x) = (x - 3)(2x + 7)/(x2 + 9x - 8). a. (3, 0), (-7, 0) b. (-3, 0), (7/2, 0) c. (3, 0), (-7/2, 0) d. none Q34. Solve the inequality algebraically. Express the solution in interval notation. (9x - 5)/(x + 2) â¤ 8 a. (-2, 13] b. (-2, 21) c. (-2, 21] d. (-2, 13) Q35. A polynomial f(x) of degree 3 whose coefficients are real numbers has the zeros -4 and 4 - 5i. Find the remaining zeros of f. a. 4, -4 + 5i b. 4, 4 + 5i c. 4 + 5i d. -4 + 5i Q36. Find the intercepts of the function f(x) = x3 + 3x2 - 4x - 12. a. x-intercepts: -2, 2, 3; y-intercept: -12 b. x-intercepts: -3, -2, 2; y-intercept: -12 c. x-intercept: -3; y-intercept: -12 d. x-intercept: -2; y-intercept: -12 Q37. Find the real solutions of the equation 3x3 - x2 + 3x - 1 = 0. a. {-3, 1/3, -1} b. {1/3} c. {1/3, -1} d. {-3, -1/3, -1} Q38. Solve the inequality algebraically. Express the solution in interval notation. x3 â¥ 27 a. (-â, 3] b. (-â, -3] âª [3, â) c. [-3, 3] d. [3, â) Q39. Find the intercepts of the function f(x) = x2(x - 1)(x - 6). a. x-intercepts: 0, -1, -6; y-intercept: 0 b. x-intercepts: 0, 1, 6; y-intercept: 6 c. x-intercepts: 0, 1, 6; y-intercept: 0 d. x-intercepts: 0, -1, -6; y-intercept: 6 Q40. Find the domain of the rational function R(x) = (-3x2)/(x2 + 2x - 15). a. {x|x â 5, 3} b. {x|x â 5, -3} c. {x|x â - 15, 1} d. {x|x â -5, 3}

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MAT 2379 Lecture Notes - Lecture 13: Quartile, Box Plot, Interquartile Range

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