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JEE • MATHEMATICS • STATISTICS

Statistics practice · Easy

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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 31-60 of 312 questions

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31 Easy

31 of 312

Understanding +4 | -1

Let

r>0

and

m

be the A. M. of the regression coefficient of

y

x

and

x

y

, then

View answer and explanation

Correct option: C

m \geq r

Option C (

m \geq r

) is correct because the arithmetic mean (m) of the regression coefficients is always greater than or equal to the geometric mean (r), which is the correlation coefficient.

32 Easy

32 of 312

Application +4 | -1

The mean weight of 150 students in 60 Kgs. The
mean weight of boys is 70 and that of girls in 55
with standard deviations 10 and 15 respectively. The
combined variance is

View answer and explanation

Correct option: A

\frac{700}{3}

Option A (700/3) is correct because it is the result of applying the combined variance formula, considering the number of students, means, and standard deviations for both boys and girls.

33 Easy

33 of 312

Application +4 | -1

On thirteen consecutive days, the number of persons booked for violating speed limit of

40 \mathrm{~km} / \mathrm{h}

were as follows:

58,61,68,57,62,50,55,62,53,54,51,59,52

The median number of speed violations per day is

View answer and explanation

Correct option: D

Option D (57) is correct because the median is the middle value when the data is arranged in ascending order.

34 Easy

34 of 312

Application +4 | -1

The weighted mean of first

n

natural number if their weight are the same as the number is-

View answer and explanation

Correct option: C

\frac{2 n+1}{3}

Option C (

\frac{{2 n+1}}{{3}}

) is correct because the weighted mean is calculated by summing the product of each number and its weight, then dividing by the sum of the weights, resulting in the given expression.

35 Easy

35 of 312

Application +4 | -1

If in a frequency distribution, the mean and median are 21 and 22 respectively, then its mode is approximately

View answer and explanation

Correct option: A

Option A (24) is correct because the mode is calculated using the empirical relationship between mean, median, and mode.

36 Easy

36 of 312

Analyzing +4 | -1

The mean deviation from mean of the observation

a,\;a + d,\;a + 2d,\; \ldots a + 2nd

View answer and explanation

Correct option: D

None of these

The correct answer is None of these because the mean deviation from the mean of the given arithmetic progression is

\frac{{n\left( {n + 1} \right)\left| d \right|}}{{\left( {2n + 1} \right)}}

, which is not among the options.

37 Easy

37 of 312

Application +4 | -1

The first of two samples has 100 items with mean 15 and

SD = 3.

If the whole group has 250 items with mean 15.6 and

SD = \sqrt {13.44}

, the SD of the second group is

View answer and explanation

Correct option: A

Option A (4) is correct because it is the standard deviation of the second group calculated using the given information about the combined group and the first group.

38 Easy

38 of 312

Application +4 | -1

In a college of 300 students every student reads 5 newspapers and every newspaper is read by 60 students. The number of newspapers are

View answer and explanation

Correct option: C

Exactly 25

Option C (Exactly 25) is correct because the number of newspapers is calculated by dividing the total number of students reading newspapers by the number of students reading each newspaper.

39 Easy

39 of 312

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.

40 Easy

40 of 312

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.

41 Easy

41 of 312

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.

42 Easy

42 of 312

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.

43 Easy

43 of 312

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.

44 Easy

44 of 312

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.

45 Easy

45 of 312

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.

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46 Easy

46 of 312

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.

47 Easy

47 of 312

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.

48 Easy

48 of 312

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.

49 Easy

49 of 312

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.

50 Easy

50 of 312

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.

51 Easy

51 of 312

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.

52 Easy

52 of 312

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.

53 Easy

53 of 312

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.

54 Easy

54 of 312

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.

55 Easy

55 of 312

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.

56 Easy

56 of 312

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.

57 Easy

57 of 312

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.

58 Easy

58 of 312

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.

59 Easy

59 of 312

Application +4 | -1

Which of the following is correct about the series

24,38,55,69,89

View answer and explanation

Correct option: C

Mean = Median

Option C (Mean = Median) is correct because the calculated mean and median of the given series are both equal to 55.

60 Easy

60 of 312

Application +4 | -1

Karl Pearson's coefficient of skewness of a distribution is 0.32 . Its

S D

is 6.5 and mean 39.6. Then, the median of the distribution is given by

View answer and explanation

Correct option: B

38.9

Option B (38.9) is correct because it is the approximate median calculated using Karl Pearson's coefficient of skewness formula.

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Review STATISTICS in your textbook or class notes, then use this set to check your understanding.

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