Download Doubtnut Today STATISTICS JEE Mains Super40 ...€¦ · 24 192503 JEE Mains Super40 Revision Series STATISTICS The mean weight of 9 items is 15. I f one more item is added

JEE Mains Super40 Revision Series

STATISTICS

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1 11408

JEE Mains Super40 Revision Series STATISTICS

The average marks of boys in a class is 52 and that of girls is 42. The average marks of boys and girlscombined is 50. The percentage of boys in the class is (1) 40 (2)20 (3) 80 (4) 60

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2 11449


The mean of the numbers a, b, 8, 5, 10 is 6 and the variance is 6.80. Then which one of the followinggives possible values of a and b? (1) (2) (3) (4)


3 11466


If the mean deviation of the numbers from their mean is 255, then the dis equal to (1) 10.0 (2) 20.0 (3) 10.1 (4) 20.2


4 11477 JEE Mains Super40 Revision Series STATISTICS

Statement 1: The variance of first n even natural numbers is Statement 2: The sum of first n

natural numbers is and the sum of squares of first n natural numbers is

a = 0, b = 7 a = 5, b = 2 a = 1, b = 6a = 3, b = 4

1, 1 + d, 1 + 2d, ..., 1 + 100d

n2 − 1

4

(nn + 1

2(n(n + 1)

2n + 1

6

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(1) Statement1 is true, Statement2 is true, Statement2 is a correct explanation for statement1 (2)Statement1 is true, Statement2 is true; Statement2 is not a correct explanation for statement1. (3)Statement1 is true, statement2 is false. (4) Statement1 is false, Statement2 is true


5 11504


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 (1) (2) 2 (3) (4)


6 11540


If the mean deviation about the median of the numbers a, is then |a| equals : (1) 2 (2)3 (3) 4 (4) 5


7 11594


All the students of a class performed poorly in Mathematics. The teacher decided to give grace marks of10 to each of the students. Which of the following statistical measures will not change even after thegrace marks were given ? (1) median (2) mode (3) variance (4)mean


8 11635


The variance of first 50 even natural numbers is (1) (2) 833 (3) 437 (4)



The mean of the data set comprising of 16 observations is 16. If one of the observation valued 16 isdeleted and three new observations valued 3, 4 and 5 are added to the data, then the mean of the

11

2

13

25

2

2a, .... . , 50a 50,

833

4

437

4

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resultant data, is : (1) 16.8 (2) 16.0 (3) 15.8 (4) 14.0


10 11700


If the standard deviation of the numbers is then which of the following is true ?


11 13680


In an experiment with 15 observations of x the following results were available one observation that was 20 was found to be wrong and it was replaced

by its correct value of 30 Then the corrected variance is (1) (2) (3) (4)


12 25233


The mean of observations is . If the first item is increased by 1, second by 2 and so on, then the

new mean is (b) (c) (d) None of these


13 41460


batsman in his 12 th inning makes a score of 63 runs and thereby increases his average score by 2. Hisaverage after the 12 th inning will be : (a) (b) (c) (d)


14 44519


The means of five observations is 4 and their variance is 5.2. If three of these observations are 1,2 and6, then the other two are 2 and 9 (b) 3 and 8 4 and 7 (d) 5 and 6



2, 3, a and 11 3.5,

∑x2 = 2830∑x = 1708.33 78 188.66 177.33

n X

X + n X +n

2X +

n + 2

2

65 39 41 53

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The algebraic sum of deviations of 10 observations measured from 16 to 7. The mean is 105 (b) 70 (c) 15.7 (d) None of these


16 71113


Coefficient of variation of a distribution is 60 and its standard deviation is 21 ,then its arithmetic mean is :(a) (b) (c) (d)


17 76144


A box contains green and yellow balls. If balls are randomly drawn, onebyone, with

replacement, then the variance of the number of green balls drawn is : (a) (b) (c) (d)


18 86892


The algebraic sum of the deviations of a set of n values from their mean is (a) (b) (c) (d)


19 122415


In a series of observations, half of them equal end remaining half equal If the S.D. of the

observationsis then equals (1) (2) (3) (4)


36 37 35 38

15 10 1012

56 4

6

25

0 n − 1 nn + 1

2n a −a.

2, |a|1

n√2 2

√2

n

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20 122417


Let bem n observations such that Then a possiblevalue of amongthe following is (1) (2) (3) (4)


21 122471


Suppose a population A has 100 observations and another population Bhas 100 observations If represent the variances of the two

populations respectively,then is (a) (b) (c) (d)


22 146854


If two random variables are related by and standard deviation of is thenstandard deviation of is (a) (b) (c) (d)


23 192469


The mean of four observations is 3. If the sum of the squares of these observations is 48 then theirstandard deviation is (1) (2) (3) (4)


x1, x2, ......xn, ∑x2i = 400 and ∑xi = 80.n 12 9 18 15

101, 102, ................ , 200151, 152, ....... .250. VA and VB

VA

VB1

9

4

4

9

2

3

x and y y = − 3x + 4 x 2y −6 6 18 3.50

√2 √3 √5 √7

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24 192503


The mean weight of 9 items is 15. If one more item is added to the series the mean becomes 16. Thevalue of 10th item is (a) (b) (c) (d)


25 193522


If in a frequency distribution, the mean and median are respectively, then its mode isapproximately (a) (b) (c) (d)


26 193524


Mean deviation of the series from its mean is (a) (b)

(c) (d)


27 216328


In a class of 100 whose average maaverage marks oflass of 100 students there are 70 boysaveragemarks in a subject are 75. If themarks of the complete class is 72, thenwhat is the average of the girls?(a) (b) (c) (d)


35 30 25 20

21 and 2220.5 22.0 24.0 25.5

a, a + d, a + 2d, ....... , a + 2nd(n + 1)d

(2n + 1)nd

2n + 1

(2n + 1)d

n(n + 1)

n(n + 1)d

2n + 1

73 65 68 74

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28 230225


The mean of 5 observations is 5 and their variance is 124. If three of the observationsare then the mean deviation from the mean of the data is (1) (b) (c) (d)


29 234236


The average income of a group of persons is and that of another group is If the number ofpersons of both group are in the ratio then average income of combined group is: (1) (vec x + vecy)/7 (3vec x + 4 vec y)/7 (4 vec x + 3vec y)/7` (4) Non of these


30 234290


The standard deviation of variate is σ. Then standard deviation of the variate where

are constants is (a) (b) (c) (a^2/c^2)sigma` (d) Non of these


31 239498


The median and standard deviation (S.D.) ofa distribution will be, If each term is increased by 2 medianand S.D. will increased by 2 (1) mediam and S.D. will increased by 2 (2) `median will increased by 2 butS.D. will remain same (3) median will remain same but S.D. will increased by 2 (4) median and S.D. willremain same


1, 2 and 6,2.4 2.8 2.5 2.6

→x

→y .

4 : 3,(2) (3)

xiaxi + b

ca, b, c

( )σa

c∣∣

∣∣σ

a

c

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32 276645


Mean of 100 items is 49. It was discovered that three items which should have been were

wrongly read as respectively. The correct mean is. (a) (b) (c) (d)


33 339058


The mean marks of 100 students were found to be 40.Later on it was discovered that a score of 53 wasmisread as 83. The corrected mean corresponding to the corrected score is: (a) (b) (c) (d)


34 1167226


A scientist is weighing each of 30 fishes. Their mean weight worked out is 30 gm and a standarddeviation of 2 gm. Later, it was found 20.that the measuring scale was misaligned and always underreported every fish weight by 2 gm. The correct mean and standard deviation(in gm) of fishes arerespectively (a) (b) (c) (d)


35 1242005


If then the standard deviation of the 9 items

is


60, 70, 80

40, 20, 50 48 821

250 80

37.5 35.6 39.738.7

28, 4 32, 2 32, 4 28, 2

9

∑i= 1

(xi − 5) = 9 and9

∑i= 1

(xi − 5)2 = 45

x1, x2, .... . , x9

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36 1450067


Coefficient of variation of two distributions are 60% and 70% and their standard deviations are 21 and16 respectively. What are their arithmetic means?


37 2500505


In a moderately asymmetrical series, the values of arithmetic mean and mode are at respectively. The value of the median is


38 2518713


The mean of 20 observations is 15. On checkingit was found that two observations were wronglycopiedas 3 and 6. If wrong observations arereplaced by correct values 8 and 4, then the correct mean is (1) (2) 1 (3) (4)


39 3640093


The average weight of a class of 24 students is 35 kg. If the weight of the teacher be included, theaverage rises by 400 g. The weight of the teacher is (a) 45 kg (b) 50 kg (c) 53 kg (d) 55 kg


20.6 and 34.1

155.15 16.15 17

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40 4037502


The median of a series is 10. Two additional observations 7 and 20 are added to series. The median ofnew series is (a) (b) (c) (d)


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Download Doubtnut Today STATISTICS JEE Mains Super40 ...€¦ · 24 192503 JEE Mains Super40 Revision Series STATISTICS The mean weight of 9 items is 15. I f one more item is added