## Statistics MCQs1) The runs scored by a batsman in 5 ODIs are 31,97,112, 63, and 12. The standard deviation is - 24.79
- 23.79
- 25.79
- 26.79
Here, first, we need to find mean = 31+97+112+12= 315/5 = 63
= 25.79 2) Find the mode of the call received on 7 consecutive day 11,13,13,17,19,23,25 - 11
- 13
- 17
- 23
3) Find the median of the call received on 7 consecutive days 11,13, 17, 13, 23,25,19 - 13
- 23
- 25
- 17
Where, n = number of terms = 7 The median is the middle value of the data sets, so first, we need to arrange the number in ascending order 11,13,13,17,19,23,25 the middle one is 7+1/2 = 4 so, the 4 4) Find the mode and median of the 9 consecutive number 12,7,8,14,21,23,27,7,11 - 12,9
- 7,9
- 7,12
- 11,9
Where n = number of terms = 9 The median is the middle value of the data sets, so first, we need to arrange the number in ascending order 7,7,8,11,12,14,21,23,27 the middle one is 9+1/2 = 5 so, the 5 5) When the Mean of a number is 18, what is the Mean of the sampling distribution? - 21
- 18
- 27
- 23
6) If the probability of hitting an object is 0.8, find the variance - 0.18
- 0.16
- 0.14
- 0.12
Given, P = 0.8 q = 1-p = 1 - 0.8 =0.2 Therefore, mean = q = 0.2 And we know that variance = 7) If the probability that an object dropped from a certain height will strike the ground is 80 percent and if 12 objects are dropped from the same place, find the mean and variance. - 9.6,1.92
- 8.6,1.92
- 9.6,1.82
- 8.6,1.82
Given, p= 80% = 0.8 and q = 1-p = 20% = 0.2 and n= 12 Therefore,
And,
8) Find the mean of tossing 4 coins - 1
- 2
- 3
- 4
Here, p = ½ and q = ½ N = 4 Therefore, 9) Variance of a constant 'x' is - 0
- x/2
- x
- 1
We know that, V(a) = = x 10) E(X) = λ is used for which distribution? - Binomial distribution
- Poisson's distribution
- Bernoulli's distribution
- Laplace distribution
11) The Mean of a constant 'x' is - 0
- x/2
- x
- 1
12) If P(x) = 0.8 and x = 3, then find the value of E(x) - 2.6
- 2.8
- 2.2
- 2.4
13) If P (1) = P (2) in Poisson's distribution, find the value of mean
14) If P (1) = λ P (5) in Poisson's distribution, find the value of mean - 33.81
- 53.81
- 63.81
- 43.81
15) Find the expectation of random variable a? - 5.71
- 4.71
- 6.71
- 8.71
We know that, E(X) = 0(1/7) + 1(2/7) + 2 (3/7) + 3(4/7) + 4(5/7) 0 + 2/7 + 6/7 + 12/7 + 20/7 = 5.71 16) If K is the Mean of Poisson distribution, then the variance is given by - K/2
- K
- K
^{2} - K
^{1/2}
17) If K is the Mean of Poisson distribution, then the standard deviation is given by - √k
- K
^{2} - K
- k/2
Therefore, Standard Deviation = √variance = √k 18) Find the arithmetic mean of the set of data: 6,1,5,8, and 10 - 4
- 5
- 6
- 7
19) Calculate the geometric Mean of 1,3,9,3 - 1
- 2
- 3
- 4
In the given question, the total number is 4, so by using the formula to determine the geometric Mean, we have,
= (81) = (3 = 3 20) Find the variance of the given data set: 3,9,5,6,7 - 1
- 2
- 3
- 4
Therefore, Then, we need to find the Variance V = (3-6) = 9+9+1+0+1 /5 = 20/5 = 4 21) Find the mean, mode and median of the given sets of data: 5,8,12,17,12,14,6,8, 12, and 10 - 11,12,10
- 10,12,13
- 11,12,13
- 10,12,11
= 12 (12 repeated 3 times in the set of data) For median, first we need to arrange the value in ascending order in the given data set: 5,6,8,8,10,12,12,12,14,17. Here, the numbers 10 and 12 are the middle values. The average of the given number is 12+10/2 = 11. Hence, 11 is the median for the given data set. So, the value of Mean, mode, and median are 10,12,11 22) Find the mean mode and median of the messages received on 7 consecutive days 7,13,5,9,6,5,10 - 7,8,9
- 8,9,9
- 8,8,9
- 6,8,9
For median, first, we need to arrange the value in ascending order in the given data set: 5,5,6,9,9,9,13. Here, the number 9 is placed in the middle. Hence, 9 is the median for the given data set. So, the value of Mean, mode, and median are 8,9,9 23) Calculate the range of the given sets of data 7,47,8,42,47,95,42,96,2 - 6
- 94
- 71
- 84
Here, Maximum value in the data sets = 96, and Minimum value = 2 Therefore, 24) Find the mean deviation according to the Mean of the given data sets 7,47,8,42,47,95,42,96,3 - 11
- 111
- 112
- 113
If we want to calculate the mean deviation according to the Mean. First, we need to calculate the Mean of the given data sets Therefore, Now, we need to find the deviation to calculate mean deviation i.e., (43-7) +(47-43) +(43-8) +(43-42) +(47-43) +( 95-47) +(43-42) +(96-43) +(43-3) = 222 So, 25) Find the mean deviation according to median of the given data sets 7,47,8,42,47,95,42,96,3 - 99
- 100
- 101
- 102
If we want to calculate the mean deviation according to the median, first, we need to calculate the median of the given data sets Therefore, to calculate the median, first, we need to arrange the number in ascending order 3,7,8,42,42,47,47,95,96 SO, Now, we need to find the deviation to calculate mean deviation according to median i.e., (42-3) +(47-7) +(42-8) +(42-42) +(42-42) +( 47-42) +(47-42) +(95-42) +(96-42) = So, 26) Find the variance of the given data sets 7,47,8,42,47,95,42,96,3 - 1028.78
- 1018.78
- 1029.78
- 1019.78
If we want to calculate the variance, first, we need to calculate the Mean of the given data sets Therefore, Now, we need to find the square of deviation to calculate variance i.e., (43-7) =1296+16+1225+1+16+2304+1+2809+1600 =9268 So, 27) Find the standard deviation of the given data sets 7,47,8,42,47,95,42,96,3 - 29.09
- 30.09
- 31.09
- 32.09
If we want to calculate the standard deviation, first, we need to calculate the Mean of the given data sets Therefore Now, we need to find the square root to calculate the variance i.e., (43-7) =1296+16+1225+1+16+2304+1+2809+1600 =9268 28) Find the coefficient of variation of the given data sets 7,47,8,42,47,95,42,96,3 - 72.64
- 74.62
- 30.39
- 78.58
If we want to calculate the coefficient, we need to calculate the Mean of the given data sets. Therefore,
Now, we need to find the square root to calculate the variance i.e., (43-7) =1296+16+1225+1+16+2304+1+2809+1600 =9268 So, 29) Find the value of λ in Poisson's distribution if the probability of getting a tail in a biased coin toss is ¼ when 8 coins are tossed. - 2
- 3
- 1
- 4
Given, Probability (P) = ¼ And we know that,
30) The Mean of a random variable K is given by equation - E(K)
- (EK)
^{2} - E
^{2}- K^{2} - None of these
31) Find the Mean of a constant k - K
- k/2
- k
^{2} - 1
Let f(x) be the random variable of the given function X Now, E(k) = ∫kf(x) = kf(x) = k(1) = k 32) Find the Variance of the constant 'K' - 1
- 0
- K
^{2} - K/2
= 33) Find the variance in a Binomial Distribution, if x, y, and z are the probability of getting success, failure, and a number of trials, respectively. - xyz
- x
^{2}yz - xy
^{2}z - x
^{2}y^{2}z^{2}
If we consider a discrete function, the variance is given by the following equation
Here, µ = Mean When we substitute X(x) = z
34) Poisson distribution is applied for - Regular Random Variable
- Constant time function
- Discrete Random Variable
- Irregular Random Variable
Poisson distribution is usually applied for discrete random variables along with Binomial distribution. The Poisson distribution expresses the probability of a given number of events occurring in a fixed interval of time and space if these events occur with a known average rate and independently since the last event. As a result, the distribution is often used in counting processes where the average rate of the events happening is known, and individual events occur independently of each other. 35) If P (1) = λ P (2) in Poisson's distribution, find the value of mean - 2
- 5
- 6
- 7
36) calculate the mean the given data set: 3,8,12,17,16,14,6,8, 16, and 10 - 11
- 12
- 13
- 14
(3+8+12+17+16+14+6+8+16+10)/ 10 = 11 37) Find the mode of the given data set: 5,8,12,17,12,12,6,8, 12, and 12 - 8
- 5
- 12
- 17
= 12 (12 repeated 5 times in the set of data) 38) Find the median of the given data set: 5,8,12,17,2,14,6,8, 13, and 7 - 5
- 2
- 8
39) If the probability of hitting a target is 0.4, find the mean and variance - 0.6,0.28
- 0.6,0.24
- 0.8, 0.22
- 0.8, 0.20
Given,
q = 1-p = 1 - 0.4 =0.6 Therefore, And we know that 40) Find the arithmetic mean of the set of data: 9,11,10,10,5,15and 10 - 11
- 1
- 10
- 13
41) Calculate the variance of the given data set: 4,7,6,3,7,3 - 2
- 4
- 6
- 8
If we want to calculate the variance, first we need to find the Mean of the given data set, Therefore, Then, we need to find the = 1 + 4 + 1 + 4 + 4 +4/6 = 18/3 = 6 42) If K denotes the expectation, the variance of a random variable X is denoted as? - (K(X)
^{2}) - 2K(X)
- K(X
^{2}) - (K(X)^{2}) - K(X)
^{2}
According to the property of Expectation
43) If K is a variance between 0 and 4. Find the value of K(X2) - 32
- 64
- 27
- 9
Integrating f(x) = X 44) Find the median of the run made by a player in 5 T20 matches, 55,44, 21, 35, 45. - 55
- 51
- 45
- 44
Where n = number of terms = 5 The median is the middle value of the data sets, so first, we need to arrange the number in ascending order 21,35,44,45,55 the middle one is 5+1/2 = 3rd number so, the 3rd number is 44 45) Find the standard deviation of the given data sets 7,2,8,11,6,13,16 - 4.64
- 4.34
- 2.34
- 3.64
If we want to calculate the standard deviation, first, we need to calculate the Mean of the given data sets Therefore, Now, we need to find the square root to calculate the variance = (Mean - each number of data sets) i.e., (9-7) =4 + 49 + 1 + 4 + 9 + 16 + 49 =132 So, 46) Find the coefficient of the given data sets 7,2,8,11,6,13,16 - 48.64
- 43.34
- 42.34
- 48.22
If we want to calculate the standard deviation, first, we need to calculate the Mean of the given data sets Therefore, Now, we need to find the square root to calculate the variance = (Mean - each number of data sets) i.e., (9-7) =4 + 49 + 1 + 4 + 9 + 16 + 49 =132 So, 47) The random variables of A and B have variances 0.4 and 0.6, respectively, and K = 4A - 2B. Find the value of K - 2.2
- 4.4
- 6.6
- 8.8
Given
And K = 4A - 2B Therefore, Var(K) = Var(4A - 2B) = Var(4A) + Var(2B) = 16 Var(A) + 4 Var(B) Var(K) = 16*0.4 + 4*0.6 = 8.8 48) The mean value of the Hypergeometric distribution is given by the equation - E(X) = n*k/N
^{2} - E(X) = n*k/N-1
- E(X) = n*k/N
- E(X) = n*k/N
^{3}
The equation gives the Mean of the Hypergeometric distribution
Where, N denotes the number of trails K denotes the number of success And, N denotes the sample size 49) The Variance of the Hypergeometric distribution is given by the equation - n* k (N-k)*(N-n)/[N
^{2}*(N-1)] - n* k (N-k)*(N-n)/[N
^{3}*(N-P)] - n* k (N-1)*(N
^{2}-n)/[N^{2}*(N-1)] - n* k (N-k)*(N
^{2}-n)/[N^{3}*(N-1)]
The variance of the Hypergeometric distribution is given by n* k (N-k)*(N-n)/[N Where, n denotes the number of trails K denotes the number of success An, N denotes the sample size. 50) Find the range of the following data sets 61,22,34,17,81,99,42,94. - 81
- 82
- 83
- 84
We know that,
Here, Maximum value in the data sets = 99, and Minimum value = 17 Therefore, Range = 99-17= 82 Next TopicEngineering Mechanics MCQ |