# Average- Aptitude Questions and Answers

 What is the range of the data given below- 20, 35, 70, 65, 45, 95, 15, 80 A) 15 B) 80 C) 45 D) 95 Correct Answer : 80 Explanation :Ordering the data from least to greatest, we get: 15, 20, 35, 45, 65, 70, 80, 95 highest - lowest = 95 - 15 = 80 The range is 80 What is the Arithmetic Mean of first 100 natural numbers? A) 50 B) 50.5 C) 51 D) 55 Correct Answer : 50.5 Explanation :Mean=(Total Sum of all the Values)/(No of Values) The Sum of first ’n' natural numbers is given by,Sum=n*(n+1)/2 then, Mean=[n*(n+1)/2] / n =n*(n+1) / 2*n So,the mean of first 100 natural numbers, Mean=100*101 / 2*100 =101/2 =50.5 Find the mean, median, mode, and range for the following list of values ? 13, 18, 13, 14, 13, 16, 14, 21, 13 A) 15, 14, 13 and 8 B) 15, 14, 14 and 13 C) 13, 13, 13 and 13 D) 15, 14, 13 and 15 Correct Answer : 15, 14, 13 and 8 Explanation :Mean :To find the mean, add all the numbers together then divide by the number of numbers. Mean = (13 + 18 + 13 + 14 + 13 + 16 + 14 + 21 + 13) / 9 = 15 Median:To find the median, order the numbers and see which one is in the middle of the list. Reordered = 13, 13, 13, 13, 14, 14, 16, 18, 21 - the middle term is 14 ie Median=14 Mode:To find the mode, order the numbers lowest to highest and see which number appears the most often. 13 is the number which appears the most often Range:To find the range, subtract the lowest number from the biggest number. Reordered = 13, 13, 13, 13, 14, 14, 16, 18, 21 Range = ( 21- 13 ) = 8 The average of the first 10 prime numbers? A) 10.1 B) 10 C) 12.9 D) 13 Correct Answer : 12.9 Explanation :First 10 prime numbers are 2,3,5,7,11,13,17,19,23,29 Average =(2+3+5+7+11+13+17+19+23+29)/10 =129/10 =12.9 Two years ago, the average age of a family of 8 members was 18 years. The average age of the family after the birth of a child is the same today. How old is the child? A) 2 years B) 1*(1/2) years C) 1 year D) 2*(1/2) years Correct Answer : 2 years Explanation :As given, after birth of child average age is same ie 18 years, hence age of child is 2 years Or 2 years back total age of 8 members = 18 * 8 = 144 years Total present age of 8 members = 144 + 2*8 = 160 years Now, a child born, average age reamin same, that is Average age of 9 people = 18 Toatl age of 9 people = 18 * 9 = 162 years. Age of child = 162 - 160 = 2 years The average of 9 full numbers is 11 but after calculation, it was seen that while computing by the mistake the 23 was written to 32. What will be the new average after making appropriate amendment? A) 10 B) 9 C) 10.1 D) 9.5 Correct Answer : 10 Explanation :The average of 9 numbers = 11 Therefore, the total is = 9*11 =99 But by mistake the 23 was written 32 So, new avarage =(99+23-32)/9 =90/9 =10 The average of first three numbers out of four numbers are 18 and the average of the last three numbers is 16. If the last number is 19, then the first number is? A) 19 B) 18 C) 20 D) 25 Correct Answer : 25 Explanation :Let the numbers are A, B ,C and D, then as given A+B+C=18*3=54 B+C+D=16*3=48 After resolving the above equations - A-D=6 the last number is 19 ie D=19 So, A=6+19 =25 The average of seven consecutive numbers is 20, then the largest number in those numbers is? A) 24 B) 23 C) 22 D) 20 Correct Answer : 23 Explanation :Let the numbers are X to ..(X+6). As given, X+(X+1)+(X+2)+(X+3)+(X+4)+(X+5)+(X+6)=20*7 7*X+21=140 7*X=119 X=17 Hence, the largest number is=(X+6) =17+6 =23 A man bought 13 items worth Rs 70, 15 items worth Rs 60 and 12 items worth 65 rupees. Average value per item is? A) 60.25 B) 64.75 C) 65.75 D) 63.25 Correct Answer : 64.75 Explanation :Average value=(13*70)+(15*60)+(12*65) / (13+15+12) =2590/40 =64.75 If the average of 20-digit X1, X2, ... X20 is Y, then what is the average of X1-101, X2-101, X3-101 ..... X20-101? A) Y-20 B) Y-101 C) 20Y D) 101Y Correct Answer : Y-101 Explanation :Average = (X1+ X2+X3 +... +X20)/20 - (101*20)/20 =Y-101 The average of 27 numbers is 60. If instead of 28 one number has changed to 82, what will be the average? A) 56 B) 58 C) 62 D) 64 Correct Answer : 62 Explanation :New average = (27*60)- 28 + 82 / 27 =1620-28+82 / 27 =1674/27 =62 A factory buys 8 machines.3 Machine A, 2 Machine B and rest Machine C. Prices of the machines are 100000, 80000 and 45000 respectively.Calculate the average cost of these machines? A) 74375 B) 75000 C) 75625 D) 72875 Correct Answer : 74375 Explanation :Average cost of all the machines =(3*100000 + 2*80000 + 3*45000) / 8 = 595000/8 = 74375 The mean of 5 numbers is 15. If one more number is included, the mean of the 6 numbers becomes 17. What is the included number? A) 24 B) 25 C) 26 D) 27 Correct Answer : 27 Explanation :Sum of these 5 numbers = Mean*Total Number = 15*5 = 75 Let the number included is x. As given 75+x / 6 = 17 75+x = 17*6 x = 102-75 x = 27 The mean marks obtained by 300 students in a subject are 60. The mean of top 100 students was found to be 80 and the mean of last 100 students was found to be 50. The mean marks of the remaining 100 students are? A) 70 B) 65 C) 60 D) 50 Correct Answer : 50 Explanation :Total marks of remaining(middle 100) students = 300*60 - 100*80 - 100*50 = 18000 - 8000 - 5000 = 18000 - 13000 = 5000 Hence, Mean marks of remaining 100 students = 5000/100 = 50 In an asymmetrical distribution, of the mean and median of the distribution are 270 and 220 respectively, then the mode of the data is? A) 120 B) 220 C) 380 D) 370 Correct Answer : 120 Explanation :Mode = 3 Median - 2 Mean = 3*220 - 2*270 = 660 - 540 = 120 Let a, b, c, d, e, f, g be consecutive even numbers and j, k, l, m, n be consecutive odd numbers. What is the average of all the numbers? A) 3(a + n) /2 B) (5l + 7d )/4 C) (a + b + m + n)/4 D) (7d + 5l) /12 Correct Answer : (7d + 5l) /12 Explanation :Let a = x (even) b = x + 2, c = x + 4, d = x + 6 e = x + 8, f = x + 10, g = x + 12 a + b + c + d + e + f + g = 7x + 42 = 7(x + 6) = 7d And j = y (odd), k = y + 2, l = y + 4, m = y + 6, n = y + 8 j + k + l + m+ n = 5y + 20 = 5( y + 4) = 5l Average of all the numbers = (7d + 5l) /12