Statistics(11th And 12th > Mathematics ) Questions and answers for exam Preparation

11th And 12th > Mathematics

STATISTICS MCQs

Total Questions : 30 | Page 1 of 3 pages

Question 1.

The range of the observations in 3, 8, 4, 9, 16, 19 is

Discuss Question

Answer: Option A. -> 16
:
A

Range = Highest observation - Lowest observation
= 19 − 3
= 16

Question 2.

The mean of 10 numbers is 12.5; the mean of the first six is 15 and the last five is 10. The sixth number is

15
12
18
none of these

Discuss Question

Answer: Option A. -> 15
:
A

L e t t h e m e a n o f t h e l a s t f o u r b e A_{2} . T h e n b y t h e f o r m u l a f o r c o m b i n e d m e a n, 12.5 = \frac{6 \times 15 + 4 \times A_{2}}{6 + 4}; o r 125 = 90 + 4 A_{2}; ∴ A_{2} = \frac{35}{4} L e t t h e s i x t h n u m b e r = x; t h e n t a k i n g t h e s i x t h n u m b e r a s a c o l l e c t i o n, t h e c o m b i n e d m e a n o f t h i s c o l l e c t i o n a n d t h e c o l l e c t i o n o f t h e l a s t f i v e i s 10, b y q u e s t i o n . ∴ B y d e f i n i t i o n o f c o m b i n e d m e a n 10 = \frac{1 \times x + 4 \times \frac{35}{4}}{1 + 4}; 50 = x + 35; ∴ x = 15 ∴ s i x t h n u m b e r = 15

Question 3.

If the coefficient of variation and standard deviation of a distribution are 2 and 0.4 respectively, then mean of the distribution is

Discuss Question

Answer: Option B. -> 20
:
B

$C . V = 2; σ = 0.4 (g i v e n) C . V = 100 \times \frac{s . d}{m e a n} 2 = \frac{100 \times 0.4}{m e a n} M e a n = \frac{40}{2} = 20$

Question 4.

If the mean of the set of number $x_{1}, x_{2} . . . x_{n}$ is $¯ x$ ,then the mean of the number $x_{i} + 2 i, 1 \leq\leq n$ is

$¯ x + 2 n$
$¯ x + n + 1$
$¯ x + 2$
$¯ x + n$

Discuss Question

Answer: Option B. ->

¯ x + n + 1

:
B

¯ x = \frac{\sum_{i = 1}^{n} x_{i}}{n} \Rightarrow \sum_{i = 1}^{n} x_{i} = n ¯ x ∴ \frac{\sum_{i}^{n} (x_{i} + 2 i)}{n} = \frac{\sum_{i = 1}^{n} x_{i} + 2 (1 + 2 + . . . + n)}{n} = \frac{n ¯ x + 2 \frac{n (n + 1)}{2}}{n} = ¯ x + (n + 1)

Question 5.

Mean deviation of the series a, a + d, a + 2d, a + 2nd from its mean is

$\frac{(n + 1) d}{(2 n + 1)}$
$\frac{(n d)}{(2 n + 1)}$
$\frac{n (n + 1) d}{(2 n + 1)}$
$\frac{2 (n + 1) d}{n (n + 1)}$

Discuss Question

Answer: Option C. ->

\frac{n (n + 1) d}{(2 n + 1)}

:
C

¯ x = \frac{\frac{2 n + 1}{2} (a + a + 2 n d))}{(2 n + 1)} = a + n d \sum | x - ¯ x | = 2 d (1 + 2 + . . . . . + n) = n (n + 1) d ∴ M . D = \frac{n (n + 1) d}{(2 n + 1)}

Question 6.

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:

2 and 9
3 and 8
4 and 7
5 and 6

Discuss Question

Answer: Option C. -> 4 and 7
:
C

Let the other two numbers be
$α a n d β .$
$¯ x = 4, N = 5 a n d \frac{\sum (x - ¯ x)^{2}}{N} = 5.2 \Rightarrow \sum (x - ¯ x)^{2} = (5.2) 5 ∴ \sum (x - ¯ x)^{2} = 26 ∴ (1 - 4)^{2} + (2 - 4)^{2} + (6 - 4)^{2} + (α - 4)^{2} + (β - 4)^{2} = 26 ∴ (α - 4)^{2} + (β - 4)^{2} = 9 A l s o, \frac{1 + 2 + 6 + α + β}{5} = 4 ∴ α + β = 20 - 9 = 11 C l e a r l y 4, 7 o n l y s a t i s f y t h e a b o v e e q u a t i o n i n α, β . H e n c e r e q u i r e d n u m b e r s a r e 4, 7.$

Question 7.

The mean deviation from the mean for the set of observations – 1, 0, 4 is

less than 3
less than 1
greater than 2.5
greater than 4.9

Discuss Question

Answer: Option A. -> less than 3
:
A

$¯ x = \frac{- 1 + 0 + 4}{3} = 1. ∴ Mean Deviation = \frac{1}{3} [| - 1 - 1 | + | 0 - 1 | + | 4 - 1 |] = 2$

Question 8.

If the S.D of a set of observations is 4 and if each observation is divided by 4, the S.D of the new set of observations will be

Discuss Question

Answer: Option D. -> 1
:
D

We know that if we multiply all numbers of a set by a constant "k" then the mean of these numbers will also be a multiple of the old mean.
And the variance of these numbers will be multiple of " $k^{2}$ ".
Since standard deviation is nothing but the square root of variance, s.d will be multiple of "k" of the old standard deviation.
We are given the s.d was 4.
So after multiplying each observation by (1/4), the s.d will also be multiplied by (1/4), thus giving the value = 4 $\times \frac{1}{4}$ = 1

Question 9.

If the mean of 3, 4, x, 7, 10 is 6, then the value of x is

Discuss Question

Answer: Option C. -> 6
:
C

6 = \frac{3 + 4 + x + 7 + 10}{5}

\Rightarrow 30 = 24 + x

\Rightarrow x = 6

Question 10.

The A.M. of a set of 50 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

36
36.5
37.5
38.5

Discuss Question

Answer: Option C. -> 37.5
:
C

$w e h a v e, \frac{\sum x_{i}}{50} = 38, ∴ \sum x_{i} = 1900 N e w v a l u e o f \sum x_{i} = 1900 - 55 - 45 = 1800 a n d n = 48 ∴ n e w m e a n = \frac{1800}{48} = \frac{450}{12} = \frac{225}{6} = 37.5.$