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