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## Sunday 21 February 2021

### CBSE Class 11 Maths - MCQ and Online Tests - Unit 15 - Statistics

#### CBSE Class 11 Maths  – MCQ and Online Tests – Unit 15 – Statistics

Every year CBSE schools conducts Annual Assessment exams for 6,7,8,9,11th standards. These exams are very competitive to all the students. So our website provides online tests for all the 6,7,8,9,11th standard’s subjects. These tests are also very effective and useful for those who preparing for any competitive exams like Olympiad etc. It can boost their preparation level and confidence level by attempting these chapter wise online tests.

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#### CBSE Class 11 Maths  – MCQ and Online Tests – Unit 15 – Statistics

Question 1.
If one of the observation is zero then geometric mean is
(a) (Sum of observation)/n
(b) (Multiplication of all observations)n
(c) (Multiplication of all observations)1/n
(d) 0

Hint:
Let the observations are 0, a, b, c, ……… up to n
Now, geometric mean = (0 Ũ a Ũ b Ũ c Ũ ……… up to n)1/n
= 0
So, geometric mean is 0

Question 2.
Which one is measure of dispersion method
(a) Renge
(b) Quartile deviation
(c) Mean deviation
(d) all of the above

Answer: (d) all of the above
Hint:
Range, Quartile deviation, Mean deviation all are the measure of dispersions method.

Question 3.
The coefficient of variation is computed by
(a) S.D/.MeanŨ100
(b) S.D./Mean
(c) Mean./S.DŨ100
(d) Mean/S.D.

Hint:
The coefficient of variation = S.D./Mean

Question 4.
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

Hint:
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

Question 5.
If mode of a series exceeds its mean by 12, then mode exceeds the median by
(a) 4
(b) 8
(c) 6
(d) 12

Hint:
Given, Mode = Mean + 12
? Mode – 12 = Mean
Now, Mode = 3ŨMedian – 2ŨMean
? Mode = 3ŨMedian – 2(Mode – 12)
? Mode = 3ŨMedian – 2ŨMode + 24
? Mode + 2ŨMode = 3ŨMedian + 24
? 3ŨMode = 3ŨMedian = 24
? Mode = Median + 8
So, mode exceeds the median by 8

Question 6.
The median and SD of a distributed are 20 and 4 respectively. If each item is increased by 2, the new median and SD are
(a) 20, 4
(b) 22, 6
(c) 22, 4
(d) 20, 6

Hint:
Since each value is increased by 2, therefore the median value is also increased by
2. So, new median = 22
Again, the variance is independent of the change of origin. So it remains the same.

Question 7.
Range of the data 4, 7, 8, 9, 10, 12, 13 and 17 is
(a) 4
(b) 17
(c) 13
(d) 21

Hint:
Give, data are: 4, 7, 8, 9, 10, 12, 13 and 17
Range = Maximum value – Minimum Value
= 17 – 4
= 13

Question 8.
If Mean = Median = Mode, then it is
(a) Symmetric distribution
(b) Asymmetric distribution
(c) Both symmetric and asymmetric distribution
(d) None of these

Hint:
In a symmetric distribution,
Mean = Median = Mode

Question 9.
If the varience of the data is 121 then the standard deviation of the data is
(a) 121
(b) 11
(c) 12
(d) 21

Hint:
Given, varience of the data = 121
Now, the standard deviation of the data = v(121) = 11

Question 10.
If the mean of the following data is 20.6, then the value of p is
x = 10 15 p 25 35
f = 3 10 25 7 5
(a) 30
(b) 20
(c) 25
(d) 10

Hint:
Mean = ? f iŨ x i /? f i
? 20.6 = (10 Ũ 3 + 15 Ũ 10 + p Ũ 25 + 25 Ũ 7 + 35 Ũ 5)/(3 + 10 + 25 + 7 + 5)
? 20.6 = (30 + 150 + 25p + 175 + 175)/50
? 20.6 = (530 + 25p)/50
? 530 + 25p = 20.6 Ũ 50
? 530 + 25p = 1030
? 25p = 1030 – 530
? 25p = 500
? p = 500/25
? p = 20
So, the value of p is 20

Question 11.
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

Hint:
Given, ?x = 12 and ?xē = 18
Now, varience = ?xē/n – (?x/n)ē
? varience = 18/10 – (12/10)ē
? varience = 9/5 – (6/5)ē
? varience = 9/5 – 36/25
? varience = (9 Ũ 5 – 36)/25
? varience = (45 – 36)/25
? varience = 9/25
? Standard deviation = v(9/25)
? Standard deviation = 3/5

Question 12.
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)

Hint:
Given, algebraic sum of of the deviation of 20 observations measured from 30 is 2
? ?(xi – 30) = 2 {1 = i = 20}
? ?xi – 30 Ũ 20 = 2
? (?xi)/20 – (30 Ũ 20)/20 = 2/20
? (?xi)/20 – 30 = 0.1
? Mean – 30 = 0.1
? Mean = 30 + 0.1
? Mean = 30.1

Question 13.
If the mean of first n natural numbers is 5n/9, then n =
(a) 5
(b) 4
(c) 9
(d) 10

Hint:
Given mean of first n natural number is 5n/9
? (n+1)/2 = 5n/9
? n + 1 = (5nŨ2)/9
? n + 1 = 10n/9
? 9(n + 1) = 10n
? 9n + 9 = 10n
? 10n – 9n = 9
? n = 9

Question 14.
Varience is independent of change of
(a) origin only
(b) scale only
(c) origin and scale both
(d) None of these

Hint:
Varience is independent of change of origin only.

Question 15.
Let x1, x2, x3, ……… , xn, be n observations and X be the arithmetic mean. Then formula for the standard deviation is given by
(a) ?(xi – mean)ē
(b) ?(xi – mean)2 /n
(c) v{?(xi – mean)ē/n}
(d) None of these

Hint:
Given, x1, x2, x3, ………. , xn be n observations and X be the arithmetic mean.
Now standard deviation = v{?(xi – mean)ē/n}

Question 16.
If a variable takes discrete values x + 4, x – 7/2, x – 5/2, x – 3, x – 2, x + 1/2, x – 1/2, x + 5 (x > 0), then the median is
(a) x – 5/4
(b) x – 1/2
(c) x – 2
(d) x + 5/4

Hint:
Given, discrete values x + 4, x – 7/2, x – 5/2, x – 3, x – 2, x + 1/2, x – 1/2, x + 5
Now, arrange them in ascending order, we get
x – 7/2, x – 3, x – 5/2, x – 2, x – 1/2, x + 1/2, x + 4, x + 5
Total observations = 8
Now, median = AM of 4th and 5th observations
= AM of (x – 2) and (x – 1/2) observations
= (x – 2 + x – 1/2)/2
= (2x – 5/2)/2
= x – 5/4

Question 17.
If covariance between two variables is 0, then the correlation coefficient between them is
(a) nothing can be said
(b) 0
(c) positive
(d) negative

Hint:
The relationship between the correlation coefficient and covariance for two variables as shown below:
r(x, y) = COV(x, y)/{sx Ũ sy}
r(x, y) = correlation of the variables x and y
COV(x, y) = covariance of the variables x and y
sx = sample standard deviation of the random variable x
sx = sample standard deviation of the random variable y
Now given COV(x, y) = 0
Then r(x, y) = 0

Question 18.
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 is
(a) 18
(b) 20
(c) 22
(d) 24

Hint:
Given mean of 100 observations is 20
Now
? xi/100 = 20 (1 = i = 100)
? ?xi = 100Ũ20
? ?xi = 2000
3 observations 21, 21 and 18 are recorded in-correctly.
So ?xi = 2000 – 21 – 21 – 18
? ?xi = 2000 – 60
? ?xi = 1940
Now new mean is
? xi/100 = 1940/97 = 20
So, the new mean is 20

Question 19.
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

Hint:
Given the difference of mode and median of a data is 24
? Mode – Median = 24
? Mode = Median + 24
Now, Mode = 3ŨMedian – 2ŨMean
? Median + 24 = 3ŨMedian – 2ŨMean
? 24 = 3ŨMedian – 2ŨMean – Median
? 24 = 2ŨMedian – 2ŨMean
? Median – Mean = 24/2
? Median – Mean = 12

Question 20.
If r is the correlation coefficient, then
(a) |r| = 1
(b) r = 1
(c) |r| = 1
(d) r = 1

Hint:
If r is the correlation coefficient, then |r| = 1

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