Mathematics NaB1102 Exercises PDF

Lecture (6) 1 Mathematics NaB1102 Dr. Mourad Semary  Outline 2  Exercises  Exercises 3 For the following grouped data, choose the correct a...

Lecture (6) 1 Mathematics NaB1102 Dr. Mourad Semary  Outline 2  Exercises  Exercises 3 For the following grouped data, choose the correct answer Class (𝑥) (0-6) (6-12) (12-18) (18-24) (24-30) f 3 4 5 7 3 1- The midpoint value for the class (6-12) is a) 6 b) 12 c) 9 d)3 6 + 12  Midpoint = 2 2- The midpoint value for the class (24-30) is a) 30 b) 27 c) 24 d)3 24 + 30  Midpoint = 2  Exercises 4 For the following grouped data, choose the correct answer Class (𝑥) (0-6) (6-12) (12-18) (18-24) (24-30) f 3 4 5 7 3 3- The value of σ 𝑓𝑖 is a) 1260 b) 22 c) 21 d)126  σ 𝑓𝑖 = 3+4+5+7+3 4- The value of ς 𝑓𝑖 is a) 1260 b) 22 c) 21 d)126  ς 𝑓𝑖 = 3 ∗ 4 ∗ 5 ∗ 7 ∗ 3  Exercises 5 For the following grouped data, choose the correct answer Class (𝑥) (0-6) (6-12) (12-18) (18-24) (24-30) f 3 4 5 7 3 5- The value of σ 𝑓𝑖 𝑥𝑖 is a) 1260 b) 4.7 ∗ 1024 c) 1267 d)348  σ 𝑓𝑖 𝑥𝑖 = (3 ∗ 3)+(4 ∗ 9) +(5 ∗ 15)+(7 ∗ 21)+(3 ∗ 27) 𝑓𝑖 6- The value of ς 𝑥𝑖 is a) 1260 b) 4.7 ∗ 1024 c) 1267 d)348 𝑓  ς 𝑥𝑖 𝑖 = 33 ∗ 94 ∗ 155 ∗ 217 ∗ 273  Exercises 6 For the following grouped data, choose the correct answer Class (𝑥) (0-6) (6-12) (12-18) (18-24) (24-30) f 3 4 5 7 3 7- The value of the mean is a) 13.23 b) 15.81 c) 12.67 d) 9.90 σ 𝑓𝑥 3 ∗ 3 + 9 ∗ 4 + 15 ∗ 5 + 21 ∗ 7 + 27 ∗ 3  𝑥ҧ = = σ𝑓 3+4+5+7+3  Exercises 7 For the following grouped data, choose the correct answer Class (𝑥) (0-6) (6-12) (12-18) (18-24) (24-30) f 3 4 5 7 3 8- The value of the harmonic mean is a) 13.23 b) 15.81 c) 12.67 d) 9.90 σ 𝑓𝑖 3+4+5+7+3  𝐻. 𝑀 = 𝑓𝑖 = 3 4 5 7 3 σ + + + + 𝑥𝑖 3 9 15 21 27  Exercises 8 For the following grouped data N=22, choose the correct answer Class (𝑥) (0-6) (6-12) (12-18) (18-24) (24-30) f 3 4 5 7 3 9- The value of the geometric mean is a) 13.23 b) 15.81 c) 12.67 d) 9.90 𝑁 22  G.M = ς 𝑥𝑓 = 33 ∗ 94 ∗ 155 ∗ 217 ∗ 273  Exercises 9 For the following grouped data N=22, choose the correct answer Class (𝑥) (0-6) (6-12) (12-18) (18-24) (24-30) f 3 4 5 7 3 10- The lower value of the mode class is a) 12 b) 6 c) 24 d) 18  The most repeated class (mode class) is (18 − 24) 11- The upper value of the mode class is a) 12 b) 6 c) 24 d) 18  The mode class (most repeated) is (18 − 24)  Exercises 10 For the following grouped data N=22, choose the correct answer Class (𝑥) (0-6) (6-12) (12-18) (18-24) (24-30) f 3 4 5 7 3 12- The mode class frequency is a) 2 b) 6 c) 4 d) 7  The frequency mode class (18-24) is 7 13- The values of ∆1 & ∆2 from mode class is a) 1 & 2 b) 5 & 3 c) 2 & 4 d) 5& 7  ∆1 = 7 − 5 & ∆2 = 7 − 3  Exercises 11 For the following grouped data N=22, choose the correct answer Class (𝑥) (0-6) (6-12) (12-18) (18-24) (24-30) f 3 4 5 7 3 14- The mode value is a) 18 b) 21 c) 7 d) 20 ∆1 2  𝑀𝑜𝑑𝑒 = 𝐿 + ∆1 +∆2 ∗ 𝐶 = 18 + ∗6 2+4 𝐿 = 18 ∆1 = 7 − 5 = 2 , ∆2 = 7 − 3 = 4 , C=24-18=6  Exercises 12 For the following grouped data N=22, choose the correct answer Class (𝑥) (0-6) (6-12) (12-18) (18-24) (24-30) f 3 4 5 7 3 15- The lower value of the median class is a) 12 b) 6 c) 24 d) 18 𝑁 22  median class is (12 − 18) which hold 2 = 2 = 11 < 3 + 4 + 5 16- The upper value of the median class is a) 12 b) 6 c) 18 d) 24 𝑁 22  median class is (12 − 18) which hold 2 = 2 = 11 < 3 + 4 + 5  Exercises 13 For the following grouped data N=22, choose the correct answer Class (𝑥) (0-6) (6-12) (12-18) (18-24) (24-30) f 3 4 5 7 3 17- The the median class frequency (𝑓𝑚𝑒𝑑 ) is a) 2 b) 7 c) 4 d) 5  The frequency of median class (12-18) is 5 18- The class width (C) of median class is a) 24 b) 5 c) 6 d) 18  The median class is (12−18) then C=18−12=6  Exercises 14 For the following grouped data N=22, choose the correct answer Class (𝑥) (0-6) (6-12) (12-18) (18-24) (24-30) f 3 4 5 7 3 19- The median value is a) 18 b) 16.8 c) 5 d) 20 𝑁 −𝑓 11 − 7  𝑚𝑒𝑑𝑖𝑎𝑛 = 𝐿 + 2 𝑓𝑚𝑒𝑑 ∗ 𝐶 = 12 + ∗6 5 𝐿 = 12, 𝑓𝑚𝑒𝑑 = 5 , 𝑓 = 4 + 3 = 7 , C=18-12=6  Exercises 15 For the following ungrouped data N=12, choose the correct answer 𝑥 30 40 50 60 𝑓 2 5 3 2 20- If σ 𝑓 (𝑥 − 𝑥)ҧ 2 = 1091.68 then the value of standard deviation is a) 13.23 b) 15.81 c) 12.67 d) 9.96 σ 𝑓 (𝑥−𝑥)ҧ 2 1091.68  𝑆= = 𝑁−1 12 − 1  Exercises 16 For the following ungrouped data N=12, choose the correct answer 𝑥 30 40 50 60 𝑓 2 5 3 2 21- If 𝑠 = 9.96 the coefficient of standard deviation is a) 0.225 b) 1.43 c) 2.67 d) 9.96 𝑆 9.96 CV= = 𝑥ҧ 44.2  Exercises 17 For the following ungrouped data N=12, choose the correct answer 𝑥 30 40 50 60 𝑓 2 5 3 2 22- The mode value is a) 5 b) 40 c) 3 d) 50 23- The median value is a) 5 b) 40 c) 3 d) 50  Try to Solve 18 For the following grouped data N= 40 Classes 𝟎 − 𝟏𝟎 𝟏𝟎 − 𝟐𝟎 𝟐𝟎 − 𝟑𝟎 𝟑𝟎 − 𝟒𝟎 𝟒𝟎 − 𝟓𝟎 Frequency f 5 9 12 7 7 a) Find mean b) Find harmonic mean e) Find geometric mean c) Calculate mode d) Calculate median. f) Find standard deviation σ 𝑓𝑖 𝑥𝑖 σ 𝑓𝑖 𝒙)𝟐 σ 𝒇 (𝒙 − ഥ ഥ 𝒙= σ 𝑓𝑖 , 𝑯. 𝑴 = 𝑓 , 𝑺= , σ 𝑖 𝑵−𝟏 𝑥𝑖 𝑁 𝑁 ∆1 − 𝑓 𝑮. 𝑴 = ς 𝑥𝑖𝑓𝑖 , 𝑴𝒐𝒅𝒆 = 𝐿 + ∗ 𝐶 , 𝑴𝒆𝒅𝒊𝒂𝒏 = 𝐿 + 2 ∗𝐶 ∆1 +∆2 𝑓𝑚𝑒𝑑