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

The mean deviation about the mean for the data arraycccccccxi & 5 & 7 & 9 & 10 & 12 & 15\ fi & 8 & 6 & 2 & 2 & 2 & 6 array is equal to:

1. 4013
2. 4213
3. 4413
4. 4613

A variable X takes values 0, 0, 2, 6, 12, 20, , n(n-1) with frequencies nC0, nC1, nC2, nC3, nC4, nC5, , nCn, respectively. If the mean of this data is 60, then its median is :

1. 56
2. 42
3. 72
4. 90

Suppose that the mean and median of the non-negative numbers 21, 8, 17, a, 51, 103, b, 13, 67, (a>b), are 40 and 21, respectively. If the mean deviation about the median is 26, then 2a is equal to :

1. 109
2. 117
3. 161
4. 131

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

If the mean of the data [figure] is 21, then k is one of the roots of the equation :

1. 2x2-23x-10=0
2. 4x2-35x+24=0
3. 2x2-19x-10=0
4. 2x2-35x+98=0

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 10 observations are 9 and 34.2, respectively. If 8 of these observations are 2, 3, 5, 10, 11, 13, 15, 21, then the mean deviation about the median of all the 10 observations is

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

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

If the mean deviation about the median of the numbers k, 2k, 3k, , 1000k is 500, then k2 is equal to :

1. 1
2. 16
3. 9
4. 4

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 the standard deviation of the observations 2, 3, 3, 4, 5, 7, a, b be 4 and 2 respectively. Then the mean deviation about the mode of these observations is :

1. 12
2. 34
3. 1
4. 2

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

Marks obtains by all the students of class 12 are presented in a freqency distribution with classes of equal width. Let the median of this grouped data be 14 with median class interval 12-18 and median class frequency 12. If the number of students whose marks are less than 12 is 18 , then the total number of students is :

1. 52
2. 44
3. 40
4. 48