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JEE • MATHEMATICS • STATISTICS

Statistics practice · Mixed difficulty

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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 451-465 of 465 questions
451 Easy
451 of 465
Application +4 | -1
Mean, mode and standard deviation of a frequency distribution are 41,45 and 8 respectively, Pearson's coefficient of skewness is
View answer and explanation
Correct option: D
-0.5
Option D (-0.5) is correct because it is the Pearson's coefficient of skewness calculated using the formula (Mean - Mode) / SD.
452 Easy
452 of 465
Application +4 | -1
The mean of 20 observations is 15 . On checking it was found that the two observations were wrongly copied as 3 and 6 . The correct values are 8 and 4 , then correct mean will be given by
View answer and explanation
Correct option: A
15.15
Option A (15.15) is correct because the correct mean is calculated by subtracting the incorrect values and adding the correct values to the original sum, then dividing by the number of observations.
453 Easy
453 of 465
Application +4 | -1
If the standard deviation of the observation −5,−4,−3−2,−1,0,1,2,3,4,5- 5, - 4, - 3 - 2, - 1,0,1,2,3,4,5 is 10\sqrt {10}. The standard deviation of observations 15,16,17,18,19,20,21,22,23,24,2515,\mathrm{ }16,\mathrm{ }17,\mathrm{ }18,\mathrm{ }19,\mathrm{ }20,\mathrm{ }21,\mathrm{ }22,\mathrm{ }23,\mathrm{ }24,\mathrm{ }25 will be
View answer and explanation
Correct option: D
None of these
Option D (None of these) is correct because adding a constant to each observation does not change the standard deviation.
454 Easy
454 of 465
Remembering +4 | -1
One of the methods of determining mode is
View answer and explanation
Correct option: C
Mode =3=3 median -2 mean
Option C (Mode =3=3 median -2 mean) is correct because this is the empirical relationship between mode, median, and mean.
455 Easy
455 of 465
Application +4 | -1
The coefficient of variation of a series is 50. Its S.D. is 21.2. Its arithmetic mean is
View answer and explanation
Correct option: D
None of these
Option D (None of these) is correct because the arithmetic mean is calculated using the coefficient of variation and standard deviation, resulting in 42.4.
456 Medium
456 of 465
Application +4 | -1
A car owner buys petrol at Rs. 7.50 , 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
View answer and explanation
Correct option: C
Rs. 7.98
Option C (Rs. 7.98) is correct because it represents the average cost per litre of petrol calculated using the harmonic mean.
457 Easy
457 of 465
Application +4 | -1
Coefficient of variation of two distribution are 60 and 70, and their standard deviations are 21 and 16, respectively. What are their arithmetic means?
View answer and explanation
Correct option: A
35,22.8535,22.85
Option A (35, 22.85) is correct because using the formula for the coefficient of variation, we can solve for the arithmetic means of the two distributions.
458 Easy
458 of 465
Understanding +4 | -1
The median and standard deviation (S.D.) of a distribution are 20 and 4 respectively. If each item is increased by 2 then
View answer and explanation
Correct option: B
Median will will go up by 2 but S.D. will remain same
Option B (Median will go up by 2 but S.D. will remain same) is correct because adding a constant to all data points shifts the median by that constant, but does not affect the standard deviation.
459 Medium
459 of 465
Understanding +4 | -1
If xˉ1\bar{x}_1 and xˉ2\bar{x}_2 are means to two distributions such that xˉ1<xˉ2\bar{x}_1 < \bar{x}_2 and xˉ\bar{x} is the mean of the combined distribution, then
View answer and explanation
Correct option: D
xˉ1<xˉ<xˉ2\bar{x}_1 < \bar{x} < \bar{x}_2
Option D (xˉ1<xˉ<xˉ2\bar{x}_1 < \bar{x} < \bar{x}_2) is correct because the mean of the combined distribution must lie between the means of the individual distributions.
460 Easy
460 of 465
Application +4 | -1
If M. D. is 12, the value of S.D. will be
View answer and explanation
Correct option: A
15
Option A (15) is correct because the standard deviation (S.D.) is related to the mean deviation (M.D.) through a constant factor, and given M.D. = 12, S.D. can be calculated.
461 Medium
461 of 465
Application +4 | -1
If the standard deviation of the numbers 2, 3, aa and 11 is 3.5, then which of the following is true?
View answer and explanation
Correct option: B
3a2−32a+84=03{a^2} - 32a + 84 = 0
Option B (3a2−32a+84=03{a^2} - 32a + 84 = 0) is correct because it is the equation derived from the given standard deviation of the numbers.
462 Easy
462 of 465
Application +4 | -1
If the coefficient of variation is 45% and the mean is 12 then its standard derivation is
View answer and explanation
Correct option: C
5.45.4
Option C (5.45.4) is correct because it is the standard deviation calculated using the coefficient of variation formula.
463 Easy
463 of 465
Application +4 | -1
The median and SD of a distribution are 20 and 4 , respectively. If each item is increased by 2 , then new median and SD\mathrm{SD} will be
View answer and explanation
Correct option: D
22,4
Option D (22,4) is correct because adding a constant to each item increases the median by the same constant, while the standard deviation remains unchanged.
464 Medium
464 of 465
Understanding +4 | -1
The median of a set of 9 distinct observations is 20.5. If each of the largest 4 observations of
the set is increased by 2, then the median of the new set
View answer and explanation
Correct option: C
Remains the same as that of the original set
Option C (Remains the same as that of the original set) is correct because the median is the middle value, and increasing the largest values doesn't affect the middle value.
465 Medium
465 of 465
Application +4 | -1
If z=ax+byz=a x+b y and rr is the correlation coefficient between xx and yy, then σz2\sigma_z^2 is equal to
View answer and explanation
Correct option: B
a2σx2+b2σy2−2abrσxσya^2 \sigma_x^2+b^2 \sigma_y^2-2 a b r \sigma_x \sigma_y
Option C (a2σx2+b2σy2+2abrσxσya^2 \sigma_x^2+b^2 \sigma_y^2+2 a b r \sigma_x \sigma_y) is correct because it represents the variance of the linear combination of two variables, including the covariance term.

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