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Class 11 Maths MCQ Questions of Statistics with Answers?

Answer 1

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Practice MCQ Questions for class 11 Maths Chapter-Wise

1. The sum of 10 items is 12 and the sum of their squares is 18. The standard deviation is

(a) 1/5
(b) 2/5
(c) 3/5
(d) 4/5

2. The algebraic sum of the deviation of 20 observations measured from 30 is 2. So, the mean of observations is

(a) 30.0
(b) 30.1
(c) 30.2
(d) 30.3

3. When tested the lives (in hours) of 5 bulbs were noted as follows: 1357, 1090, 1666, 1494, 1623. The mean of the lives of 5 bulbs is

(a) 1445
(b) 1446
(c) 1447
(d) 1448

4. If mode of a series exceeds its mean by 12, then mode exceeds the median by

(a) 4
(b) 8
(c) 6
(d) 12

5. Range of the data 4, 7, 8, 9, 10, 12, 13 and 17 is

(a) 4
(b) 17
(c) 13
(d) 21

6. If the difference of mode and median of a data is 24, then the difference of median and mean is

(a) 12
(b) 24
(c) 8
(d) 36

7. If the mean of first n natural numbers is 5n/9, then n =

(a) 5
(b) 4
(c) 9
(d) 10

8. When an observation in the sata is ……………., then its geometric mean is zero. 

(a) 0
(b) 1
(c) 2
(d) 3

9. The mean of a group of 100 observations was found to be 20. Later on, it was found that three observations were incorrect, which was recorded as 21, 21 and 18. Then the mean if the incorrect observations are omitted

(a) 18
(b) 20
(c) 22
(d) 24

10. Variance is independent of change of

(a) origin only
(b) scale only
(c) origin and scale both
(d) None of these

11.  Consider the following statements:

(1) If the correlation coefficient r_xy = 0, then the two lines of regression are parallel to each other.

(2) If the correlation coeficient r_xy =+1, then the two lines of regression are perpendicular to each other? Which of the above statements is/are correct?

(a) 1 only
(b) 2 only
(c) Both 1 and 2
(d) Neither 1 nor 2

12. If A.M. and G.M. of two numbers are 16 and 8; then H.M. is 

(a) 3
(b) 5
(c) 4
(d) 8

13. Which one is measure of dispersion method

(a) Standard Deviation,Median, Range
(b) Standard Deviation,Mode,Range
(c) Standard Deviation,Variance, Range
(d) Mean,Mode,Median

14. Range of data 7,8,2,1,3,13,18 is?

(a) 15
(b) 17
(c) 13
(d) 10

15. The mean of six numbers is 30. If one number is excluded, the mean of the remaining numbers is 29. The excluded number is 

(a) 29
(b) 30
(c) 35
(d) 45

16. The mean of a set of 20  observation is 19.3 . The mean is reduced by 0.5 when a new observation is added to the set. The new observation is

(a) 19.8
(b) 8.8
(c) 9.5
(d) 30.8

17. 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) 30.8

18.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) 9

19. Standard deviation for first 10  natural numbers is

(a) 5.5
(b) 3.87
(c) 2.97
(d) 2.87

20. In a batch of 15 students, if the marks of 10 students who passed are 70, 50, 95, 40, 60, 70, 80, 90, 75, 80 then the median marks of all the 15 students is:

(a) 40
(b) 50
(c) 60
(d) 70

Answer 2

1. Answer: (c) 3/5

Explanation: Given, ∑x = 12 and ∑x² = 18

Now, varience = ∑x²/n – (∑x/n)²

⇒ varience = 18/10 – (12/10)²

⇒ varience = 9/5 – (6/5)²

⇒ varience = 9/5 – 36/25

⇒ varience = (9 × 5 – 36)/25

⇒ varience = (45 – 36)/25

⇒ varience = 9/25

⇒ Standard deviation = \(\sqrt\frac{9}{25}\)

⇒ Standard deviation = 3/5

2. Answer: (b) 30.1

Explanation: Given, algebraic sum of of the deviation of 20 observations measured from 30 is 2

⇒ ∑(x_i – 30) = 2 {1 ≤ i ≤ 20}

⇒ ∑x_i – 30 × 20 = 2

⇒ (∑x_i)/20 – (30 × 20)/20 = 2/20

⇒ (∑x_i)/20 – 30 = 0.1

⇒ Mean – 30 = 0.1

⇒ Mean = 30 + 0.1

⇒ Mean = 30.1

3. Answer: (b) 1446

Explanation: Given, lives (in hours) of 5 bulbs were noted as follows: 1357, 1090, 1666, 1494, 1623

Now, mean = (1357 + 1090 + 1666 + 1494 + 1623)/5

= 7230/5

= 1446 

4. Answer: (b) 8

Explanation: Given, Mode = Mean + 12

⇒ Mode – 12 = Mean

Now, Mode = 3×Median – 2×Mean

⇒ Mode = 3×Median – 2(Mode – 12)

⇒ Mode = 3×Median – 2×Mode + 24

⇒ Mode + 2×Mode = 3×Median + 24

⇒ 3 × Mode 

= 3 × Median 

= 24

⇒ Mode = Median + 8

So, mode exceeds the median by 8

5. Answer: (c) 13

Explanation: Give, data are: 4, 7, 8, 9, 10, 12, 13 and 17

Range = Maximum value – Minimum Value

= 17 – 4

= 13

6. Answer: (a) 12

Explanation: Given the difference of mode and median of a data is 24

⇒ Mode – Median = 24

⇒ Mode = Median + 24

Now, Mode = 3×Median – 2×Mean

⇒ Median + 24 = 3×Median – 2×Mean

⇒ 24 = 3×Median – 2×Mean – Median

⇒ 24 = 2×Median – 2×Mean

⇒ Median – Mean = 24/2

⇒ Median – Mean 

= 12

7. Answer: (c) 9

Explanation: Given mean of first n natural number is 5n/9

⇒ (n+1)/2 = 5n/9

⇒ n + 1 = (5n×2)/9

⇒ n + 1 = 10n/9

⇒ 9(n + 1) = 10n

⇒ 9n + 9 = 10n

⇒ 10n – 9n = 9

⇒ n = 9

8. Answer: (a) 0

Explanation: When an observation in the sata is 0 then its geometric mean is zero.

9. Answer: (b) 20

Explanation: Given mean of 100 observations is 20

Now

∑ x_i/100 = 20 (1 = i = 100)

⇒ ∑x_i = 100 × 20

⇒ ∑x_i = 2000

3 observations 21, 21 and 18 are recorded in-correctly.

So ∑x_i = 2000 – 21 – 21 – 18

⇒ ∑x_i = 2000 – 60

⇒ ∑x_i = 1940

Now new mean is

∑ xi/100 = 1940/97 

= 20

So, the new mean is 20

10. Answer: (a) origin only

Explanation: Changing origin is same as adding some constant to values and if we add a constant to values, the dispersion of the values from the mean is not changed, so the variance is not affected and remains the same. But if we multiply our values by a constant. Therefore it is independent of origin but not of scaling.

Answer 3

11. Answer: (d) Neither 1 nor 2

Explanation: If r = 0⟹ lines do not have anything common and hence, lines of regression are perpendicular. when r =1⟹ then the lines superimpose one another and hence, lines of regression are parallel/co-incident. So, both statements are wrong. 

12. Answer: (c) 4

Explanation: We know the relation between Arithmetic Mean, Harmonic Mean, and Geometric Mean of Two Numbers: 

A.M. × H.M. = (G.M.)²

⇒16× H.M. = 8²

⇒16× H.M. = 6⁴

⇒ H.M.= 4

13. Answer: (c) Standard Deviation,Variance,Range

Explanation: Standard Deviation, Variance, and Range are measures of dispersion but the Mean, Mode, and Median are the measure of central tendency.

14. Answer: (b) 17

Explanation: 7,8,2,1,3,13,18,

range of data = (maximum − minimum)

= (18−1)

= 17

15. Answer: (c) 35

Explanation: Sum of 6 numbers = 30 × 6 = 180

Sum of remaining 5 numbers = 29 × 5 = 145

∴ Excluded number 

= 180 - 145 

= 35

16. Answer: (b) 8.8

Explanation: Mean of 20 observations =19.3

Sum of 20 observations = 19.3 × 20 =386

Let the new term added =x

Sum after including new term = 386 + x

Mean = \(=\frac{386+x}{21}\)​= 18.8

Therefore, x = 8.8

17. Answer: (a) 9

Explanation: Let a₁,a₂,a₃,a₄ and a₅ be five quantities

Then a₁+a₂+a₃+a₄+a₅ = 30 (given)

Also given that

a₁+a₂+a₃ =12

Now a₄ + a₅ =18 Thus the average of a₄ and a₅ will be

\(\frac{a_4+a_5}{2}\)

= 18/5

= 9

18. Answer: (b) 6

Explanation: Since 6 occurs most of the times in the given series.

∴ Mode of the given series = 6

19. Answer: (d) 2.87

Explanation: Standard deviation of first n natural number is

\(=\sqrt\frac{n^2-1}{12}\)

\(=\sqrt\frac{10^2-1}{12}\)

= 2.87

20. Answer: (c) 60

Explanation: As given marks of 10 students out of 15 in the ascending order are 40, 50, 60, 70, 70, 75, 80, 80, 90, 95

Total number of terms = 15 and 5 students who failed are below 40 marks, median

\(=\frac{n+1}{2}\) th term

8th  term = 60

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