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

11th Grade > Mathematics

STATISTICS MCQs

Total Questions : 30 | Page 1 of 3 pages

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 2.

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 3.

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 4.

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 5.

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

s increased by 2
is decreased by 2
is two times the original median
remains the same as that of the original set

Discuss Question

Answer: Option D. -> remains the same as that of the original set
:
D
We know that median is found when we arrange the observations in ascending or descending order. And if the number of observations are odd then it is the

\frac{n + 1}{2} t h

term.
Since on arranging 9 observations 5th will be the median.
On changing 4 of any side won't affect the median and it'll remain same.

Question 6.

The mean of 5 numbers is 18. If one number is excluded, their mean becomes 16. Then the excluded number is

Discuss Question

Answer: Option C. -> 26
:
C

Sum of total number $= 18 \times 5 = 90$
                After one number excluded
                Sum of total number $= 16 \times 4 = 64$
                Then, excluded number is $90 - 64 = 26$

Question 7.

If the median and mode of 4 observations is 4, 6 and the sum of squares of observations is 48. Then
standard deviation is

$\sqrt{2}$
4
$\sqrt{3}$
$\sqrt{5}$

Discuss Question

Answer: Option C. ->

\sqrt{3}

:
C

Given that median = 4 and mode = 6. We know that
Mean - mode = 3 (Mean - Median)
Mean - 6 = 3 (Mean - 4)
$¯ x - 6 = 3 ¯ x - 12$
$¯ x = 3$
$σ^{2} = \frac{\sum x_{i}^{2}}{n} - {(\frac{\sum x^{i}}{n})}^{2} = \frac{48}{4} - (3)^{2} = 3$ $∴ σ = \sqrt{3}$

Question 8.

The mean weight per student in a group of seven students is 55 kg if the individual weights of 6 students are 52, 58, 55, 53, 56 and 54; then weight of the seventh student is

55 kg
60 kg
57 kg
50 kg

Discuss Question

Answer: Option C. -> 57 kg
:
C
Total weight of 7 students is

= 55 \times 7 = 385 k g

Sum of weight of 6 students

= 52 + 58 + 55 + 53 + 56 + 54 = 328 k g

∴

Weight of seventh student

= 385 - 328 = 57 k g .

Question 9.

The mean of a set of observation is $¯ ¯ ¯ x$ .If each observation is divided by $α α \neq 0$ , and then is increased by 10,
then the mean of the new set is

$\frac{¯ ¯ ¯ x}{α}$
$\frac{¯ ¯ ¯ x + 10}{α}$
$\frac{¯ ¯ ¯ x + 10 α}{α}$
$α ¯ ¯ ¯ x + 10$

Discuss Question

Answer: Option C. ->

\frac{¯ ¯ ¯ x + 10 α}{α}

:
C
Let

x_{1}, x_{2} \dots \dots, x_{n}

be n observations.

Then ¯ ¯ ¯ x = \frac{1}{n} \sum x_{i}

let y_{i} = \frac{x_{i}}{α} + 10

¯ ¯ ¯ y = \frac{1}{n} n \sum i y_{i}

And, ¯ ¯ ¯ y = \frac{1}{n} [(n \sum i \frac{x_{i}}{α} + 10. n]

\Rightarrow ¯ ¯ ¯ y = \frac{1}{α} ¯ ¯ ¯ x + 10

= \frac{¯ ¯ ¯ x + 10 α}{α} .

Question 10.

If the coefficient of variation of data pertaining to goals scored by two teams A and B in a football season are 2.5 and 7.2 respectively, then which of the following statements i strue?

Team B is more consistent than team A.
Two teams are equally consistent.
Team A is more consistent than team B.
The s.ds. of team A and team B are $\frac{1}{25}, \frac{1}{72} .$

Discuss Question

Answer: Option C. -> Team A is more consistent than team B.
:
C
We know that, lesser is the coefficient of variation, the data is more consistent.
Since C.V. of the team A is 2.5, which is less than the C.V. of team B, we can conclude that team A is more Consistent.