Statistics and Dispersion

Sum of first three numbers = 141 Sum of last three numbers = 174 Since the third number is common in both, so difference will be 33.

Whole numbers start from 0; hence n whole numbers means n-1 natural numbers. Sum first n-1 natural numbers is {(n-1)(n-1+1)}/2 ; Average is ((n-1)*n)/(2*n) , Average is (n-1)/2.

Average of consecutive integers is always middle term. So, the average of first 129 terms is (129 + 1)/2= 65^th term, which is n. Average of 137 terms is (137 + 1)/2 = 69^th term. So, 69^th term is 65^th term + 2*4 = n + 8.

Since the average is 8 more than the actual, the second number will increase by 72 (9 x 8) by interchanging the digits. If 'ab' is the second number, then 10a + b + 72 = 10b+ a, i.e. 9 (b - a) = 72b - a = 8 The possible number 'ab' is 19. Since the second number is 19, the first number is 18. So, X = 18

Sum of 5 consecutive odd numbers (avg. m) = 5m Sum of 7 consecutive odd numbers (avg. n) = 7n So, resultant avg. = (5m + 7n)/12

Required average = 9(1 + 2 + 3 +.................. + 30)/30                                   = (9*30*31)/(30*2)                                   = 279/2                                   = 139.5

(20 + 27 + 28 + x) /4 = 25, Or x = 25 Therefore, this option is correct.

16 + 24 + 28 + 36 + 45 + 14 + 19 + 34 = 216. Arithmetic Mean = 216 / 8 = 27

Total exposures = (3000*6) + (3000*3) = 27000 Total audience reach = 3000 + 3000 = 6000 Average frequency = 27000 / 6000 = 4.5

If the average of 7 numbers is 16, then the sum of numbers must be,  112. If average of first 3 numbers is 14, then the sum of numbers must be 42. And if the average of the next 3 numbers is 18, the sum of numbers must be 54. Now, 112 - 42 - 54 = 16. Hence, the last number is 16.

 Suppose the 3 numbers are A, B and C, so A + B = 2 x 4 = 8 ----------------- (1) B + C = 2 x 5 = 10 --------------- (2) A + C = 2 x 6 = 12 --------------- (3) On adding (1), (2) and (3), we get A + B + C = 15. Therefore, average = 15/3 = 5 

Total sum of 43 numbers = (45 × 32) – (30 + 45) = 1440 – 75 = 1365 Average = 1365/43 = 31.7

Fourth number = (5 x 6 + 5 x 6 – 5 x 9) = (30 + 30 - 45) = 15 Incorrect option

The total of 9 results = 9 x 50 = 450 The total of first 5 results = 5 x 49 = 245 The total of last 5 results = 5 x 52 = 260 The 5th result is common to both; 5th result = 245 + 260 - 450 = 55.

(Average of the remaining 48 numbers = 50 X 38 - 45 - 5548 = (1900 - 100) ÷ 48 = 1800/48 = 37.5)