Statistics

A set of four observations has mean 1 and variance 13. Another set of six observations has mean 2 and variance 1. Then, the variance of all these 10 observations is equal to :

1. 5.96
2. 6.14
3. 6.04
4. 6.24

A data consists of 20 observations x1, x2, , x20. If i=120 (xi+5 )2=2500 and i=120 (xi-5 )2=100, then the ratio of mean to standard deviation of this data is :

1. 2 : 1
2. 3 : 1
3. 3 : 2
4. 4 : 1

Let the mean and the variance of seven observations 2, 4, , 8, , 12, 14, < , be 8 and 16 respectively. Then the quadratic equation whose roots are 3 +2 and 2 +1 is :

1. x2-35x+306=0
2. x2-41x+420=0
3. x2-45x+506=0
4. x2-37x+342=0

For 10 observations x1, x2, , x10, if i=110 (xi+2 )2=180 and i=110 (xi-1 )2=90, then their standard deviation is :

1. 2
2. 3
3. 2 2
4. 3

The mean and variance of n observations are 8 and 16, respectively. If the sum of the first (n-1) observations is 48 and the sum of squares of the first (n-1) observations is 496, then the value of n is :

1. 21
2. 16
3. 13
4. 7

The mean and variance of a data of 10 observations are 10 and 2, respectively. If an observation in this data is replaced by , then the mean and variance become 10.1 and 1.99, respectively. Then + equals

1. 15
2. 10
3. 5
4. 20

Let X = \x N : 1 x 19\ and for some a, b R, Y = \ax + b : x X\. If the mean and variance of the elements of Y are 30 and 750, respectively, then the sum of all possible values of b is

1. 20
2. 100
3. 80
4. 60

Let the mean and variance of 8 numbers −10, −7, −1, x, y, 9, 2, 16 be 72 and 2934, respectively. Then the mean of 4 numbers x, y, x + y + 1, |x − y| is :

1. 11
2. 9
3. 10
4. 12

If the mean and the variance of the data array|l|c|c|c|c| Class & 4-8 & 8-12 & 12-16 & 16-20 \ Frequency & 3 & & 4 & 7 \ array are and 19 respectively, then the value of + is :

1. 21
2. 19
3. 18
4. 20

Let the mean and variance of 7 observations 2, 4, 10, x, 12, 14, y, x > y, be 8 and 16 respectively. Two numbers are chosen from \1, 2, 3, x - 4, y, 5\ one after another without replacement, then the probability, that the smaller number among the two chosen numbers is less than 4, is :

1. 45
2. 35
3. 25
4. 13

The mean and standard deviation of 100 observations are 40 and 5.1, respectively. By mistake one observation is taken as 50 instead of 40. If the correct mean and the correct standard deviation are and respectively, then 10( + ) is equal to

1. 447
2. 445
3. 449
4. 451

Let the Mean and Variance of five observations x1 = 1, x2 = 3, x3 = a, x4 = 7 and x5 = b, a > b, be 5 and 10 respectively. Then the Variance of the observations n + xn, n = 1, 2, , 5 is

1. 17
2. 16
3. 16.4
4. 17.4

If the mean and the variance of 6, 4, a, 8, b, 12, 10, 13 are 9 and 9.25 respectively, then a + b + ab is equal to :

1. 103
2. 106
3. 100
4. 105

Let x1, x2, , x10 be ten observations such that i=110(xi - 2) = 30, i=110(xi - )2 = 98, > 2, and their variance is 45. If and 2 are respectively the mean and the variance of 2(x1 - 1) + 4 , 2(x2 - 1) + 4 , , 2(x10 - 1) + 4 , then 2 is equal to :

1. 100
2. 90
3. 120
4. 110

For a statistical data x1, x2, , x10 of 10 values, a student obtained the mean as 5.5 and i=110xi2=371. He later found that he had noted two values in the data incorrectly as 4 and 5, instead of the correct values 6 and 8, respectively. The variance of the corrected data is

1. 5
2. 7
3. 9
4. 4

If the variance of the frequency distribution array|c|c|c|c|c|c|c| x & c & 2c & 3c & 4c & 5c & 6c \ f & 2 & 1 & 1 & 1 & 1 & 1 \ array is 160, then the value of c N is

1. 5
2. 8
3. 6
4. 7

The mean and standard deviation of 20 observations are found to be 10 and 2, respectively. On rechecking, it was found that an observation by mistake was taken 8 instead of 12. The correct standard deviation is

1. 1.94
2. 3.96
3. 3.86
4. 1.8

Consider 10 observations x1, x2, , x10 such that i=110 (xi- )=2 and i=110 (xi- )2=40, where , are positive integers. Let the mean and the variance of the observations be 65 and 8425 respectively. Then is equal to :

1. 2
2. 1
3. 52
4. 32

Let the mean and the variance of 6 observations a, b, 68, 44, 48, 60 be 55 and 194, respectively. If a>b, then a+3b is

1. 180
2. 210
3. 190
4. 200

If the mean and variance of five observations are 245 and 19425 respectively and the mean of the first four observations is 72, then the variance of the first four observations is equal to

1. 54
2. 45
3. 1054
4. 7712

Let a1, a2, a10 be 10 observations such that k=110 ak=50 and k<j ak aj=1100. Then the standard deviation of a1, a2, , a10 is equal to :

1. 5
2. 115
3. 10
4. 5