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JEE • MATHEMATICS • STATISTICS

Statistics practice · Mixed difficulty

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Practice format and chapter quiz

These sets use single-correct-answer MCQs. They do not cover every JEE Main or JEE Advanced question format and are not full-length mock papers.

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Showing 61-90 of 465 questions

61 Easy

61 of 465

Application +4 | -1

Standard deviation of the first

2n + 1

natural numbers is equal to

View answer and explanation

Correct option: C

\sqrt {\frac{{n\left( {n + 1} \right)}}{3}}

The correct answer is C (

\sqrt {\frac{{n\left( {n + 1} \right)}}{3}}

) because it is the standard deviation formula for the first

2n+1

natural numbers.

62 Medium

62 of 465

Understanding +4 | -1

Let

x_1, x_2, \ldots, x_n

\mathrm{n}

observations, and let

\bar{x}

be their arithmetic mean and

\sigma^2

be the variance.

Statement-1: Variance of

2 x_1, 2 x_2, \ldots, 2 x_n

4 \sigma^2

.

Statement-2: Arithmetic mean

2 x_1, 2 x_2, \ldots, 2 x_n

4 \bar{x}

View answer and explanation

Correct option: D

Statement-1 is true, statement-2 is false.

Option D is correct. Statement-1 is true because variance is multiplied by the square of the constant, and Statement-2 is false because the arithmetic mean is multiplied by 2, not 4.

63 Easy

63 of 465

Application +4 | -1

Which of the following is correct for data

-1,0,1,2

3,5,5,6,8,10,11

View answer and explanation

Correct option: D

Mode = Median

Option D (Mode = Median) is correct because both the mode and median of the data are 5.

64 Easy

64 of 465

Application +4 | -1

If the first quartile is 104 and quartile deviation is 18 , then the third quartile is

View answer and explanation

Correct option: B

140

Option B (140) is correct because the third quartile is calculated using the quartile deviation formula.

65 Easy

65 of 465

Application +4 | -1

Let the observations

{x_i}\left( {1 \le i \le 10} \right)

satisfy the equations,

\sum\limits_{i = 1}^{10} {\left( {{x_i} - 5} \right) = 10}

and

\sum\limits_{i = 1}^{10} {{{\left( {{x_i} - 5} \right)}^2} = 40.}

\mu

and

\lambda

are the mean and the variance of the observations,

{x_1} - 3,\,{x_2} - 3,.....,{x_{10}} - 3,

then the ordered pair

\left( {\mu ,\lambda } \right)

is equal to

View answer and explanation

Correct option: C

(3,3)

Option C (3,3) is correct because it accurately calculates the mean and variance of the transformed observations based on the given data.

66 Easy

66 of 465

Application +4 | -1

The mean height of 25 male workers in a factory is

61 \mathrm{~cm}

and the mean height of 35 female workers in the same factory is

58 \mathrm{~cm}

. The combined mean height of 60 workers in the factory is

View answer and explanation

Correct option: A

59.25

Option A (59.25) is correct because it is the result of calculating the combined mean using the weighted average formula.

67 Easy

67 of 465

Application +4 | -1

The sum of squares of deviations for 10 observations taken from mean 50 is 250 . The coefficient of variation is

View answer and explanation

Correct option: A

10 \%

Option A (10%) is correct because it is the coefficient of variation calculated from the given data.

68 Medium

68 of 465

Application +4 | -1

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:

View answer and explanation

Correct option: C

4 and 7

Option C (4 and 7) is correct because these values satisfy both the mean and variance conditions given in the problem.

69 Medium

69 of 465

Application +4 | -1

If the mean of the data :

7,8,9,7,8,7, \lambda, 8

is 8 , then the variance of this data is

View answer and explanation

Correct option: D

Option D (1) is correct. First, find the value of lambda using the mean. Then, calculate the variance using the formula.

70 Medium

70 of 465

Remembering +4 | -1

Angle between two lines of regression is given by

View answer and explanation

Correct option: B

{\tan ^{ - 1}}\left( {\frac{{{b_{yx}}.{b_{xy}} - 1}}{{{b_{yx}} + {b_{xy}}}}} \right)

Option B (

{\tan ^{ - 1}}\left( {\frac{{{b_{yx}}.{b_{xy}} - 1}}{{{b_{yx}} + {b_{xy}}}}} \right)

) is correct because it represents the correct formula for calculating the angle between two regression lines using their regression coefficients.

71 Easy

71 of 465

Application +4 | -1

The mean age of a combined group of men and women is 25 yrs. If the mean age of the group of men is 26 and that of the group of women is 21, then the percentage of men and women in the group is

View answer and explanation

Correct option: B

80,\;20

Option B (

80,\;20

) is correct because by using the combined mean formula, we can find the percentage of men and women in the group.

72 Easy

72 of 465

Application +4 | -1

For a symmetrical distribution

Q_1=25

and

Q_3=45

, then median is

View answer and explanation

Correct option: B

Option B (35) is correct because in a symmetrical distribution, the median is the average of the first and third quartiles.

73 Easy

73 of 465

Understanding +4 | -1

The sum of squares of deviations from mean is

View answer and explanation

Correct option: A

Least

Option A (Least) is correct because the sum of squares of deviations is minimized when deviations are taken from the mean.

74 Medium

74 of 465

Application +4 | -1

The mean height of 25 male workers in a factory is
161 cms, and the mean height of 35 female workers
in the same factory is 158 cms. The combined mean
height of 60 workers in the factory is

View answer and explanation

Correct option: A

159.25

Option A (159.25) is correct because the combined mean is calculated by taking the weighted average of the means of the two groups.

75 Easy

75 of 465

Application +4 | -1

The arithmetic mean of 10 observations is 12.45 . If each reading is increased by 5 , then resulting mean is increased by

View answer and explanation

Correct option: A

Option A (5) is correct because adding a constant to each observation increases the mean by the same constant.

Explore Other Chapters in MATHEMATICS

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SEQUENCE OF SERIES 1764 MCQs DEFINITE INTEGRATION 1443 MCQs MATRICES 1363 MCQs INDEFINITE INTEGRATION 1179 MCQs PROBABILITY 1146 MCQs COMPLEX NUMBERS 980 MCQs

76 Easy

76 of 465

Application +4 | -1

If a variable takes discrete values

x + 4,\;x - \frac{7}{2},\;x - \frac{5}{2},\;x - 3,\;x - 2,\;x + \frac{1}{2},\;x - \frac{1}{2},\;x + 5,\;(x > 0)

, then the median is

View answer and explanation

Correct option: A

x - \frac{5}{4}

Option A (

x - \frac{5}{4}

) is correct because it is the median calculated after arranging the given values in ascending order and averaging the 4th and 5th terms.

77 Easy

77 of 465

Application +4 | -1

In a series of

2 n

observations, half of them equal

a

and remaining half equal

-a

. If the standard deviation of the ovservations is 2 , then

|a|

equals

View answer and explanation

Correct option: A

Option A (2) is correct because the standard deviation of the given series directly leads to the absolute value of 'a' being equal to 2.

78 Medium

78 of 465

Application +4 | -1

If the sum of the deviation 50 observation from 30 is 50, then the mean of these observations is

View answer and explanation

Correct option: D

Option D (31) is correct. The mean is calculated by using the sum of deviations from 30 to find the sum of the observations and then dividing by the number of observations.

79 Medium

79 of 465

Analyzing +4 | -1

Correlation coefficient

r

of two variables

x

and

y

is positive, when

View answer and explanation

Correct option: A

\sigma_{x+y} > \sigma_{x-y}

Option A (

\sigma_{x+y} > \sigma_{x-y}

) is correct because a positive correlation coefficient implies that the variance of the sum is greater than the variance of the difference.

80 Easy

80 of 465

Understanding +4 | -1

When the origin is changed, then the coefficient of correlation

View answer and explanation

Correct option: C

Remains fixed

Option C (Remains fixed) is correct because the coefficient of correlation is independent of the change of origin.

81 Easy

81 of 465

Application +4 | -1

The arithmetic means of a set of observations is

\bar{x}

. If each observation is divided by

\beta

and then it is increased by 12 , then the mean of the new series is

View answer and explanation

Correct option: A

\frac{\bar{x}}{\beta}+12

Option A (

\frac{\bar{x}}{\beta}+12

) is correct because dividing each observation by

\beta

and adding 12 affects the mean in the same way.

82 Easy

82 of 465

Application +4 | -1

The median of a series is 10. Two additional observations 7 and 20 are added to series. The median of new series is

View answer and explanation

Correct option: C

Option D (10) is correct because adding two additional observations does not change the median if they are on either side of the median.

83 Medium

83 of 465

Application +4 | -1

The standard deviation for the scores 1, 2, 3, 4, 5, 6 and 7 is 2. Then, the standard deviation of 12, 23, 34, 45, 56 , 67 and 78 is

View answer and explanation

Correct option: C

Option C (22) is correct because the standard deviation of a linearly transformed variable is the original standard deviation multiplied by the absolute value of the transformation factor.

84 Easy

84 of 465

Application +4 | -1

The coefficient of correlation between

x

and

y

is 1 , then coefficient of correlation between

x

and

x+y

View answer and explanation

Correct option: A

Option A (1) is correct because if the coefficient of correlation between x and y is 1, then y is a linear function of x, and the correlation between x and x+y will also be 1.

85 Easy

85 of 465

Application +4 | -1

For a series the value of mean deviation is 15, the most likely value of its quartile derivation is

View answer and explanation

Correct option: A

12.5

Option A (12.5) is correct because the quartile deviation is calculated using the relationship between mean deviation and standard deviation, and quartile deviation and standard deviation.

86 Easy

86 of 465

Application +4 | -1

The mean of 30 given numbers, when it is given that the mean of 10 of them is 12 and the mean of the remaining 20 is 9, is equal to

View answer and explanation

Correct option: B

Option B (10) is correct because the mean of the combined group is calculated using the weighted average formula.

87 Easy

87 of 465

Application +4 | -1

n=10, \bar{x}=12, \sum x^2=1530

, then the coefficient of variation is

View answer and explanation

Correct option: C

25 \%

Option C (25 %) is correct because the coefficient of variation is calculated by dividing the standard deviation by the mean and multiplying by 100.

88 Medium

88 of 465

Application +4 | -1

If the forces of 12,5 and 13 unit-wt balance at a point, two of them are inclined at

View answer and explanation

Correct option: C

90^{\circ}

Option C,

90^{\circ}

, is correct because the forces satisfy the Pythagorean theorem, indicating a right angle between the 5 and 12 unit forces.

89 Medium

89 of 465

Application +4 | -1

If the s.d. of

n

observations

x_1, x_2, \ldots, x_n

is 4 and another set of

n

observations

y_1, y_2, \ldots, y_n

is 3, the s.d. of

n

observations

x_1-y_1, x_2-y_2, \ldots, x_n-y_n

View answer and explanation

Correct option: D

None of these

Option D (None of these) is correct because the standard deviation of the difference of two sets of observations depends on the covariance between the two sets, which is not given.

90 Easy

90 of 465

Analyzing +4 | -1

\theta

is the angle between two regression lines with correlation coefficient

y

, then

View answer and explanation

Correct option: B

sin\;\theta \le 1 - {\gamma ^2}

Option B (

sin\\;\theta \le 1 - {\gamma ^2}

) is correct because it represents the upper bound of the sine of the angle between two regression lines based on the correlation coefficient.

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