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Statistics and Probability

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Q 1. A car owner buys petrol at Rs. {tex} 7.50 , {/tex} Rs. 8.00 and Rs. 8.50 per litre for 3 successive years. If he spends Rs. 4000 each year, then the average cost per litre of petrol is

{tex} R s .8 {/tex}

Rs. 8.25

Rs. 7.98

None of these

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Q 2. The algebraic sum of deviations of a set of values from the arithmetic mean is

0

1

Dependent on mean

None of these

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Q 3. The mean annual salaries paid to 1000 employees of a company was Rs. 3400 . The mean annual salaries paid to male and female employees were Rs. 200 and Rs. 4200 , respectively. The percentage of males and females employed by the company are

{tex} 50,50 {/tex}

{tex} 40,60 {/tex}

{tex} 70,30 {/tex}

{tex} 20,80 {/tex}

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Q 4. One of the methods of determining mode is

Mode {tex} = 2 {/tex} median {tex} - 3 {/tex} mean

Mode {tex} = 2 {/tex} median {tex} + 3 {/tex} mean

Mode {tex} = 3 {/tex} median {tex} - 2 {/tex} mean

Mode {tex} = 3 {/tex} median {tex} + 2 {/tex} mean

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Q 5. The average weight of 25 boys was calculated to be 78.4{tex} \mathrm { kg } {/tex} . It was later discovered that one weight was misread as 69{tex} \mathrm { kg } {/tex} instead of 96{tex} \mathrm { kg } {/tex} . The correct average is

79{tex} \mathrm { kg } {/tex}

79.48{tex} \mathrm { kg } {/tex}

81.32{tex} \mathrm { kg } {/tex}

None of these

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Q 6. The mean of following frequency table is {tex} 50 . {/tex}

{tex} \begin{array} { | c | c | } \hline \text { Class } & { \text { Frequency } } \\ \hline 0 - 20 & { 17 } \\ { 20 - 40 } & { f _ { 1 } } \\ { 40 - 60 } & { 32 } \\ { 60 - 80 } & { f _ { 2 } } \\ { 80 - 80 } & { 19 } \\ \hline \text { Total } & { 120 } \\ \hline \end{array} {/tex}

The missing frequencies are

{tex} 28,24 {/tex}

{tex} 24,36 {/tex}

{tex} 36,28 {/tex}

None of these

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Q 7. The A.M. of {tex} n {/tex} numbers of a series is {tex} \overline { X } . {/tex} If the sum of first {tex} ( n - 1 ) {/tex} terms is {tex} k , {/tex} then the {tex} n {/tex} th number is

{tex} \overline { X } - k {/tex}

{tex} n \overline { X } - k {/tex}

{tex} \overline { X } - n k {/tex}

{tex} n \overline { X } - n k {/tex}

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Q 8. If a variable takes the discrete value {tex} \alpha + 4 , \alpha - 7 / 2 , \alpha - 5 / 2 , \alpha - 3 , {/tex} {tex} \alpha - 2 , \alpha + 1 / 2 , \alpha - 1 / 2 , \alpha + 5 , ( \alpha > 0 ) , {/tex} then the median is

{tex} \alpha - 5 / 4 {/tex}

{tex} \alpha - 1 / 2 {/tex}

{tex} \alpha - 2 {/tex}

{tex} \alpha + 5 / 4 {/tex}

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Q 9. If a variate {tex} X {/tex} is expressed as a linear function of two variates {tex} U {/tex} and {tex} V {/tex} in the form {tex} X = a U + b V , {/tex} then mean {tex} \overline { X } {/tex} of {tex} X {/tex} is

{tex} a \overline { U } + b \overline { V } {/tex}

{tex} \overline { U } + \overline { V } {/tex}

{tex} b \overline { U } + a \overline { U } {/tex}

None of these

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Q 10. If {tex} a {/tex} and {tex} b {/tex} are two positive numbers, then

{tex} \mathrm { AM } \leq \mathrm { GM } \geq \mathrm { HM } {/tex}

{tex} \mathrm { AM } \geq \mathrm { GM } \leq \mathrm { HM } {/tex}

{tex} \mathrm { AM } \leq \mathrm { GM } \leq \mathrm { HM } {/tex}

{tex} \mathrm { AM } \geq \mathrm { GM } \geq \mathrm { HM } {/tex}

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Q 11. You are provided with the following raw data of two variable {tex} x {/tex} and {tex} y . {/tex}

{tex} \Sigma x = 235 , \Sigma y = 250 , \Sigma x ^ { 2 } = 6750 , \Sigma y ^ { 2 } = 6840 {/tex}. Ten pairs of values are included in the survey. The standard deviation are

{tex} 11.08,7.68 {/tex}

{tex} 11.02,7.58 {/tex}

{tex} 11.48,7.48 {/tex}

None of these

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Q 12. The best average of dealing a qualitative data is

Mean

Median

Mode

Harmonic Mean

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Q 13. The geometric mean of 6 observations was calculated as {tex} 13 . {/tex} It was later observed that one of the observation was recordedas 28 instead of {tex} 36 . {/tex} The correct geometric mean is

{tex} \left( \frac { 9 } { 7 } \right) ^ { 1 / 6 } {/tex}

3 {tex} \left( \frac { 9 } { 7 } \right) ^ { 1 / 6 } {/tex}

13 {tex} \left( \frac { 9 } { 7 } \right) ^ { 1 / 6 } {/tex}

13

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Q 14. The mean deviation about the median of the series of batsman in ten innings {tex} 34,38,42,44,46,48,54,55,56,76 {/tex} is

8.5

7.6

8

None of these

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Q 15. Median of {tex} 16,10,14,11,9,8,12,6,5 {/tex} is

10

12

11

14

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Q 16. The average marks of boys in a class are {tex}52{/tex} and that of girls is {tex} 42 . {/tex} The average marks of boys and girls combined is {tex} 50 . {/tex} The percentage of boys in the class is

{tex}40{/tex}

{tex}20{/tex}

{tex}80{/tex}

{tex}60{/tex}

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Q 17. The mean of the numbers {tex} a , b , 8,5,10 {/tex} is {tex}6{/tex} and the variance is {tex} 6.80 . {/tex} Then which one of the following gives possible values of {tex} a {/tex} and {tex} b ? {/tex}

{tex} a = 0 , b = 7 {/tex}

{tex} a = 5 , b = 2 {/tex}

{tex} a = 1 , b = 6 {/tex}

{tex} a = 3 , b = 4 {/tex}

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Q 18. If the mean deviation of number {tex} 1,1 + d , 1 + 2 d , \ldots , 1 + 100 d {/tex} from their mean is {tex} 255 , {/tex} then {tex} d {/tex} is equal to

{tex}10{/tex}

{tex}20{/tex}

{tex}10.1{/tex}

{tex}20.2{/tex}

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Q 19. Statement-1: The variance of first {tex} n {/tex} even natural numbers is {tex} \frac { n ^ { 2 } - 1 } { 4 } {/tex} .

Statement-2: The sum of first n natural numbers is {tex} \frac { n ( n + 1 ) } { 2 } {/tex} and the sum of squares of first n natural numbers is {tex} \frac { n ( n + 1 ) ( 2 n + 1 ) } { 6 } {/tex} .

Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement- 1

Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement- 1

Statement-1 is true, Statement- 2 is false

Statement-1 is false, Statement-2 is true

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Q 20. For two data sets, each of size {tex}5{/tex} , the variances are given to be {tex}4 {/tex} and {tex}5{/tex} and the corresponding means are given to be {tex}2{/tex} and {tex} 4 , {/tex} respectively. The variance of the combined data set is

{tex} \frac { 11 } { 2 } {/tex}

{tex}6{/tex}

{tex} \frac { 13 } { 2 } {/tex}

{tex} \frac { 5 } { 2 } {/tex}

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Q 21. If the mean deviation about the median of the numbers {tex} a , 2 a {/tex} , {tex} \ldots , 50 a {/tex} is {tex} 50 , {/tex} then {tex} | a | {/tex} equals

{tex}3{/tex}

{tex}4{/tex}

{tex}5{/tex}

{tex}2{/tex}

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Q 22. All the students of a class performed poorly in Mathematics. The teacher decided to give grace marks of 10 to each of the

students. Which of the following statistical measures will not change even after the grace marks were given?

Median

Mode

Variance

Mean

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Q 23. A pair of fair dice is thrown independently three times. The probability of getting a score of exactly 9 twice is

{tex}1 / 729 {/tex}

{tex}8 / 9 {/tex}

{tex}8 / 729 {/tex}

{tex} 8/ 243 {/tex}

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Q 24. Two aeroplanes I and II bomb a target in succession. The probabilities of of I and II scoring a hit correctly are 0.3 and 0.2, respectively. The second plane will bomb only if the first misses the target. The probability that the target is hit by the second plane is

0.06

0.14

0.3

0.7

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Q 25. An urn contains nine balls of which three are red, four are blue and two are green. Three balls are drawn at random without replacement from the urn. The probability that the three balls have different colour is

{tex} \frac { 2 } { 7 } {/tex}

{tex} \frac { 1 } { 21 } {/tex}

{tex} \frac { 2 } { 23 } {/tex}

{tex} \frac { 1 } { 3 } {/tex}

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