Please refer to Assignments Class 11 Mathematics Statistics Chapter 15 with solved questions and answers. We have provided Class 11 Mathematics Assignments for all chapters on our website. These problems and solutions for Chapter 15 Statistics Class 11 Mathematics have been prepared as per the latest syllabus and books issued for the current academic year. Learn these solved important questions to get more marks in your class tests and examinations.

**Statistics Assignments Class 11 Mathematics**

**Question. The relationship between the correlation coefficient r and the regression coefficients bxy and byx is: **

(a) r = 1/2 (b_{xy} + b_{yx})

(b) r = √b_{xy}.b_{yx}

(c) r = (b_{xy}.b_{yx})^{2}

(d) r = b_{xy} + b_{yx}

## Answer

B

**Question. The harmonic mean of 4, 8, 16 is **

(a) 6.4

(b) 6.7

(c) 6.85

(d) 7.8

## Answer

C

**Question. A student obtain 75%, 80% and 85% in three subjects. If the marks of another subject are added, then his average cannot be less than: **

(a) 60%

(b) 65%

(c) 80%

(d) 90%

## Answer

B

**Question. The (a)M. of a 50 set of numbers is 38. If two numbers of the set, namely 55 and 45 are discarded, the (a)M. of the remaining set of numbers is: **

(a) 38.5

(b) 37.5

(c) 36.5

(d) 36

## Answer

B

**Question. The average of n numbers x _{1}, x_{2}, x_{3},…, xn is M. If xn is replaced by x’, then new average is **

## Answer

B

**Question. If μ is the mean of distribution (y1 , f1) then Σ f(yi −μ) = ? C**

(a) M.(d)

(b) S.(d)

(c) 0

(d) Relative frequency

**Question. For the L.P. problem Mi z = 2x + y subject to 5x+10y≤50, x + y ≥1, y ≤ 4 and x, y ≥ 0 , z = ? **

(a) 0

(b) 1

(c) 2

(d) 1/2

## Answer

B

**Question. The minimum value of objective function c = 2x + 2y in the given feasible region, is **

(a) 134

(b) 40

(c) 38

(d) 80

## Answer

D

**Question. In an experiment with 15 observations on x, the following results were available Σx ^{2} = 2830,Σx =170. On observation that was 20 was found to be wrong and was replaced by the correct value 30. Then the corrected variance is: **

(a) 78.00

(b) 188.66

(c) 177.33

(d) 8.33

## Answer

A

**Question. The S.(d) of a variate x is σ. The S.(d) of the variate ax+b/c where a, b, c are constant, is: **

## Answer

B

**Question. Covariance (x, y) between x and y, if Σx =15,Σy = 40, Σx.y =110, n = 5 is **

(a) 22

(b) 2

(c) – 2

(d) None of these

## Answer

C

**Question. Let x _{1} x_{2} x_{3}….. x_{n} be the rank of n individuals according to character A and y_{1} , y_{2} y_{3}….. yn the ranks of same individuals according to other character B such that x_{1} + y_{1} = n + for i =1,2,3,…,n .Then the coefficient of rank correlation between the characters A and B is **

(a) 1

(b) 0

(c) – 1

(d) None of these

## Answer

C

**Question. If the covariance between x and y is 10 and the variance of x and y are 16 and 9 respectively, then the coefficient of correlation between x and y is: **

(a) 0.61

(b) 0.79

(c) 0.83

(d) 0.93

## Answer

C

**Question. If the regression equations of the variables x and y be x = 19.13 – 0.83y and y = 11.64 – 0.50x, then the correlation coefficient between x and y is: **

(a) 0.66

(b) – 0.64

(c) 0.001

(d) – 0.001

## Answer

B

**Question. The two lines of regression are 2x − 7 y + 6 = 0 and 7x − 2y +1 = 0. The correlation coefficient between x and y is **

(a) – 2/7

(b) 2/7

(c) 4/49

(d) None of these

## Answer

B

**Question. Shaded region is represented by **

(a) 4x − 2y ≤ 3

(b) 4x − 2y ≤ −3

(c) 4x − 2y ≥ 3

(d) 4x − 2y ≥ −3

## Answer

B

**Question. The range of following set of observations 2, 3, 5, 9, 8, 7, 6, 5, 7, 4, 3 is: **

(a) 11

(b) 7

(c) 5.5

(d) 6

## Answer

B

**Question. For a given distribution of marks mean is 35.16 and its standard deviation is 19.76. The co-efficient of variation is **

(a) 35.16 /19.76

(b) 19.76 /35.16

(c) 35.16 /19.76 x 100

(d) 19.76 /35.16 x 100

## Answer

D

**Question. For the constraint of a linear optimizing function 1 2 z=x +x ,given by 1 2 1 2 x + x ≤1, 3x + x ≥ 3 and 1 2 x , x ≥ 0 ? **

(a) There are two feasible regions

(b) There are infinite feasible regions

(c) There is no feasible region

(d) None of these

## Answer

C

**Question. In a series of 2n observations, half of them equal to a and remaining half equal to –(a) If the standard deviation of the observations is 3, then |a| equals? **

(a) √2/n

(b) √2

(c) 3

(d) 1/n

## Answer

C

**Question. The S.(d) of a variate x is σ. The S.(d) of the variate ax+b/c where a, b, c are constant, is: **

(a) (a/c)σ

(b) |a/c|σ

(c) (a^{2}/c^{2})σ

(d) None of these

## Answer

B

**Question. The true statement for the graph of in-equations 3x + 2y ≤ 6 and 6 x + 4y ≥ 20 , is: **

(a) Both graphs are disjoint

(b) Both do not contain origin

(c) Both contain point (1, 1)

(d) None of these

## Answer

A

**Question. The vertices of a feasible region of the above question are **

(a) (0, 18), (36, 0)

(b) (0, 18), (10, 13)

(c) (10, 13), (8, 14)

(d) (10, 13), (8, 14), (12, 12)

## Answer

C

**Question. The maximum value of objective function in the above question is: **

(a) 100

(b) 92

(c) 95

(d) 94

## Answer

C

**Question. For the L.P. problem Min z = −x1 + 2x such that -x _{1} + 3x_{2} ≤ 0 , x_{1} − x_{2} ≤ 6 , x1 − x2 ≤ 2 and 1 2 x , x ≥ 0 , x_{1} = ? **

(a) 2

(b) 8

(c) 10

(d) 12

## Answer

A

**Question. The S.(d) of 5 scores 1, 2, 3, 4, 5 is: **

(a) 2/5

(b) 3/5

(c) √2

(d) √3

## Answer

C

**Question. If Q.(d) is 16, the most likely value of S.(d) will be: **

(a) 24

(b) 42

(c) 10

(d) None of these

## Answer

A

**Question. The mean deviation from the mean for the set of observations –1, 0, 4 is: **

(a) √14/3

(b) 2

(c) 2/3

(d) None of these

## Answer

B

**Question. The means of five observations is 4 and their variance is 5.2. If three of these observations are 1, 2 and 6, then the other two are **

(a) 2 and 9

(b) 3 and 8

(c) 4 and 7

(d) 5 and 6

## Answer

C

**Question. For (2n+1) observations x1 ,− x1 , x2 , -x2 ,……xn − xn and 0 where x’s are all distinct. Let S.(d) and M.(d) denote the standard deviation and median respectively. Then which of the following is always true: **

(a) S.(d) < M.(d)

(b) S.(d) > M.(d)

(c) S.(d) = M.(d)

(d) Nothing can be said in general about the relationship of S.(d) and M.(d)

## Answer

B

**Question. The variance of α, β and γ is 9, then variance of 5α, 5β and 5γ is: **

(a) 45

(b) 9/5

(c) 5/9

(d) 225

## Answer

D

**Question. What is the standard deviation of the following series? **

Measurements | 0-10 | 10-20 | 20-30 | 30-40 |

Frequency | 1 | 3 | 4 | 2 |

(a) 81

(b) 7.6

(c) 9

(d) 2.26

## Answer

C

**Question. The quartile deviation of daily wages (in Rs.) of 7 persons given below 12, 7, 15, 10, 17, 19, 25 is: **

(a) 14.5

(b) 5

(c) 9

(d) 4.5

## Answer

D

**Question. The median of a set of 9 distinct observation is 20.5. If each of the largest 4 observations of the set is increased by 2, then the median of the new set is**

(a) increased by 2

(b) decreased by 2

(c) two times the original median

(d) remains the same as that of original set

## Answer

D

**Question. The mode of the following series 3, 4, 2, 1, 7, 6, 7, 6, 8, 6, 5 is**

(a) 5

(b) 6

(c) 7

(d) 8

## Answer

B

**Question. Find the mean and variance for the following data****6, 7, 10, 12, 13, 4, 8, 12**

(a) mean = 9, variance = 9.25

(b) mean = 3, variance = 7.5

(c) mean = 7, variance = 12

(d) mean = 9, variance = 12.5

## Answer

A

**Question. The average of 5 quantities is 6, the average of three of them is 4, then the average of remaining two numbers is :**

(a) 9

(b) 6

(c) 10

(d) 5

## Answer

A

**Question. Let a, b, c, d and e be the observations with mean m and standard deviation s. The standard deviation of the observations a + k, b + k, c + k, d + k and e + k is**

(a) s

(b) ks

(c) s + k

(d) s/k

## Answer

A

**Question. The arithmetic mean of a set of observations is x̄ . If each observation is divided by α then it is increased by 10, then the mean of the new series is:**

## Answer

C

**Question. The standard deviation of 5 scores 1, 2, 3, 4, 5 is √a . The value of ‘a’ is**

(a) 2

(b) 3

(c) 5

(d) 1

## Answer

A

**Question. If x _{1}, x_{2}, …., x_{n} are n values of a variable X and y_{1}, y_{2}, …., y_{n }are n values of variable Y such that y_{i} = ax_{i} + b; i = 1, 2, …, n, then write Var(Y) in terms of Var(X).**

(a) var (Y) = var (X)

(b) var (Y) = a var (X)

(c) var (Y) = a2 var (X)

(d) var (X) = a2 var (Y)

## Answer

C

**Question. The sum of the squares of deviations for 10 observations taken from their mean 50 is 250. Then, the coefficient of variation is**

(a) 10%

(b) 40%

(c) 50%

(d) None of these

## Answer

A

**Question. The observations 29, 32, 48, 50, x, x + 2, 72, 78, 84, 95 are arranged in ascending order. What is the value of x if the median of the data is 63?**

(a) 61

(b) 62

(c) 62.5

(d) 63

## Answer

B

**Question. Find the mean deviation about the mean for the data****4, 7, 8, 9, 10, 12, 13, 17**

(a) 3

(b) 24

(c) 10

(d) 8

## Answer

A

**Question. For two data sets, each of size 5, the variances are given to be 4 and 5 and the corresponding means are given to be 2 and 4, respectively. The variance of the combined data set is**

(a) 11/2

(b) 6

(c) 13/2

(d) 5/2

## Answer

A

**Question. The mean of 100 observations is 50 and their standard deviation is 5. The sum of squares of all observation is**

(a) 50000

(b) 250000

(c) 252500

(d) 255000

## Answer

C

**STATEMENT TYPE QUESTIONS**

**Question. Which of the following is/are true about the range of the data?****I. It helps to find the variability in the observations on the basis of maximum and minimum value of observations.****II. Range of series = Minimum value – Maximum value. ****III. It tells us about the dispersion of the data from a measure of central tendency.**

(a) Only I is true

(b) II and III are true

(c) I and II are true

(d) All are true

## Answer

A

**Question. Consider the following statements :****I. Mode can be computed from histogram****II. Median is not independent of change of scale****III. Variance is independent of change of origin and scale.****Which of these is / are correct ?**

(a) (I), (II) and (III)

(b) Only (II)

(c) Only (I) and (II)

(d) Only (I)

## Answer

C

**Question. Statement-I: The series having greater CV is said to be less variable than the other.****Statement-II: The series having lesser CV is said to be more consistent than the other.**

(a) Only Statement I is true

(b) Only Statement II is true

(c) Both statements are true

(d) Both statements are false

## Answer

B

**Question. If x̄ _{1} and σ_{1} are the mean and standard deviation of the first distribution and x̄_{2} and σ_{2} are the mean and standard deviation of the second distribution.**

**I. CV (1st distribution) = σ**

_{1}/x̄_{1 }x 100**II. CV (2nd distribution) = x̄**

_{2}/σ_{2 }x 100**III. For x̄**

_{1}= x̄_{2}, the series with lesser value of standard deviation is said to be more variable than the other.**IV. For x̄**

_{1}= x̄_{2}, the series with greater value of standard deviation is said to be more consistent than the other.(a) Only I is true

(b) III and IV are true

(c) I, III and IV are true

(d) All are true

## Answer

A

**Question. If x is the mean and σ ^{2} is the variance of n observations x_{1}, x_{2}, …., x_{n}, then which of the following are true for the observations ax_{1}, ax_{2}, ax_{3}, …., ax_{n}? **

**I. Mean of the observations is x̄/a .**

**II. Variance of the observations is σ**

^{2 }/ a^{2}.**III. Mean of the observations is ax .**

**IV. Variance of the observations is a**

^{2}σ^{2}.(a) I and II are true

(b) I and IV are true

(c) II and III are true

(d) III and IV are true

## Answer

D

**Question. Consider the following statements :****I. Measures of dispersion Range, Quartile deviation, mean deviation, variance, standard deviation are****measures of dispersion ****Range = Maximum value – minimum values****II. Mean deviation for ungrouped data**

M.D. (x̄) = | x_{i} – x̄ |/n

M.D. (M) = | x_{i} – M |/n**III. Mean deviation for grouped data**

M.D. ( x̄ ) = ∑ f_{i} | x_{i} – x̄ |/N

M.D. (M) = f_{i} | x_{i} – M |/N

where N = f_{i}**Which of the above statements are true?**

(a) Only (I)

(b) Only (II)

(c) Only (III)

(d) All of the above

## Answer

D

**Question. Consider the following data which represents the runs scored by two batsmen in their last ten matches as****Batsman A : 30, 91, 0, 64, 42, 80, 30, 5, 117, 71****Batsman B : 53, 46, 48, 50, 53, 53, 58, 60, 57, 52****Which of the following is/are true about the data?****I. Mean of batsman A runs is 53.****II. Median of batsman A runs is 42.****III. Mean of batsman B runs is 53.****IV. Median of batsman B runs is 53.**

(a) Only I is true

(b) I and III are true

(c) I, III and IV are true

(d) All are true

## Answer

C