JEE Mathematics Statistics MCQs Set 08

Download JEE MCQs for JEE Mathematics: Statistics

Review structured MCQ sets for JEE Mathematics Statistics. Built according to official JEE guidelines, these downloadable questions support daily revision and core concept reinforcement.

Chapter-wise Objective Questions: Statistics

Navigate directly to the 50 objective questions for Statistics using the digital viewer below. Each practice set includes verified answer keys, allowing students to instantly cross-check their work and identify areas requiring further revision.

Multiple Choice Questions

Question 1: The median of 18, 35, 10, 42, 21 is
(a) 20
(b) 19
(c) 21
(d) 22
Show Answer & Explanation

Answer: (c) 21

Explanation:
1. Arrange in order: 10, 18, 21, 35, 42.
2. With 5 values the median is the 3rd, i.e. 21.

Teacher's Note:
1. Sort first.

Question 2: The mean of the numbers a, b, 8, 5, 10 is 6 and the variance is 6.80. Then which of the following gives possible values of a and b?
(a) \( a=0,b=7 \)
(b) \( a=5,b=2 \)
(c) \( a=1,b=6 \)
(d) \( a=3,b=4 \)
Show Answer & Explanation

Answer: (d) \( a=3,b=4 \)

Explanation:
1. Mean 6 gives \( a+b+23=30 \), so \( a+b=7 \).
2. Variance \( =\frac15\left[(a-6)^2+(b-6)^2+4+1+16\right] \); for \( a=3,b=4 \) this is \( \frac{9+4+4+1+16}{5}=6.8 \). Other options give 11.6, 7.6 and 9.2.

Teacher's Note:
1. Use the mean to get a + b, then test the variance.

Question 3: The mean deviation about the mean for the data 4, 7, 8, 9, 10, 12, 13, 17 is
(a) 3
(b) 24
(c) 10
(d) 8
Show Answer & Explanation

Answer: (a) 3

Explanation:
1. Mean \( =\frac{80}{8}=10 \).
2. Absolute deviations: 6, 3, 2, 1, 0, 2, 3, 7, total 24. Mean deviation \( =\frac{24}{8}=3 \).

Teacher's Note:
1. Mean deviation = sum of |x - mean| / n.

Question 4: Find the mean deviation about the mean for the data: x = 5, 10, 15, 20, 25 with frequencies 7, 4, 6, 3, 5.
(a) 6
(b) 7.3
(c) 8
(d) 6.32
Show Answer & Explanation

Answer: (d) 6.32

Explanation:
1. N = 25 and mean \( =\frac{35+40+90+60+125}{25}=14 \).
2. \( \sum f|x-14|=63+16+6+18+55=158 \), so the mean deviation \( =\frac{158}{25}=6.32 \).

Teacher's Note:
1. Find the mean, then the frequency-weighted absolute deviations.

Question 5: Find the mean and variance for the data 6, 7, 10, 12, 13, 4, 8, 12.
(a) mean = 9, variance = 9.25
(b) mean = 3, variance = 7.5
(c) mean = 7, variance = 12
(d) mean = 9, variance = 12.5
Show Answer & Explanation

Answer: (a) mean = 9, variance = 9.25

Explanation:
1. Sum \( =72 \) so the mean is 9.
2. Squared deviations: 9, 4, 1, 9, 16, 25, 1, 9, total 74. Variance \( =\frac{74}{8}=9.25 \).

Teacher's Note:
1. Variance is the mean squared deviation.

Question 6: The lives (in hours) of 5 bulbs were noted as 1357, 1090, 1666, 1494, 1623. The mean deviation (in hours) from their mean is
(a) 178
(b) 179
(c) 220
(d) 356
Show Answer & Explanation

Answer: (a) 178

Explanation:
1. Mean \( =\frac{7230}{5}=1446 \).
2. Absolute deviations: 89, 356, 220, 48, 177; total 890. Mean deviation \( =\frac{890}{5}=178 \).

Teacher's Note:
1. Compute the mean first.

Question 7: The variance of the numbers 3, 7, 10, 18, 22 is equal to
(a) 12
(b) 6.4
(c) \( \sqrt{49.2} \)
(d) 49.2
Show Answer & Explanation

Answer: (d) 49.2

Explanation:
1. Mean \( =\frac{60}{5}=12 \).
2. Squared deviations: 81, 25, 4, 36, 100, total 246. Variance \( =\frac{246}{5}=49.2 \) (the standard deviation would be \( \sqrt{49.2} \)).

Teacher's Note:
1. Variance is the square of the standard deviation.

Question 8: The mean deviation from the mean of the following data: marks 0-10, 10-20, 20-30, 30-40, 40-50 with number of students 5, 8, 15, 16, 6 is
(a) 10
(b) 10.22
(c) 9.86
(d) 9.44
Show Answer & Explanation

Answer: (d) 9.44

Explanation:
1. Mid-points 5, 15, 25, 35, 45; N = 50 and mean \( =\frac{1350}{50}=27 \).
2. \( \sum f|x-27|=110+96+30+128+108=472 \), so the mean deviation \( =\frac{472}{50}=9.44 \).

Teacher's Note:
1. Use class mid-points.

Question 9: Two batsmen's scores in their last ten matches: A: 30, 91, 0, 64, 42, 80, 30, 5, 117, 71. B: 53, 46, 48, 50, 53, 53, 58, 60, 57, 52. Which of the following is/are true? I. Mean of A is 53. II. Median of A is 42. III. Mean of B is 53. IV. Median of B is 53.
(a) Only I is true
(b) I and III are true
(c) I, III and IV are true
(d) All are true
Show Answer & Explanation

Answer: (c) I, III and IV are true

Explanation:
1. A: sum 530, mean 53. Ordered scores 0, 5, 30, 30, 42, 64, 71, 80, 91, 117 have median \( \frac{42+64}{2}=53 \), so II (42) is false.
2. B: sum 530, mean 53, and the ordered scores 46, 48, 50, 52, 53, 53, 53, 57, 58, 60 give median 53. So I, III, IV are true.

Teacher's Note:
1. Sort each list for the median.

Question 10: Which of the following is/are true about the range of the data? I. It helps to find the variability on the basis of the maximum and minimum values. II. Range = maximum value - minimum value. III. It tells us about the dispersion of the data from a measure of central tendency.
(a) Only I is true
(b) II and III are true
(c) I and II are true
(d) All are true
Show Answer & Explanation

Answer: (c) I and II are true

Explanation:
1. I and II describe the range correctly.
2. The range uses only the two extreme values, not a central value, so III is false.

Teacher's Note:
1. The range ignores the centre.

Question 11: Statement I: the mean deviation about the mean for the data 4, 7, 8, 9, 10, 12, 13, 17 is 3.5. Statement II: the mean deviation about the mean for the data 38, 70, 48, 40, 42, 55, 63, 46, 54, 44 is 8.5.
(a) Only Statement I is true
(b) Only Statement II is true
(c) Both statements are true
(d) Both statements are false
Show Answer & Explanation

Answer: (d) Both statements are false

Explanation:
1. First data: mean 10, total absolute deviation 24, mean deviation \( \frac{24}{8}=3 \), not 3.5.
2. Second data: mean 50, absolute deviations total 84, mean deviation 8.4, not 8.5.

Teacher's Note:
1. Compute both mean deviations.

Question 12: Consider the data: size 20, 21, 22, 23, 24 with frequency 6, 4, 5, 1, 4. I. Mean is 22.65. II. Mean deviation is 1.25. III. Mean is 21.65. IV. Mean deviation is 2.25.
(a) I and II are true
(b) II and III are true
(c) I and III are true
(d) III and IV are true
Show Answer & Explanation

Answer: (b) II and III are true

Explanation:
1. N = 20. Mean \( =\frac{120+84+110+23+96}{20}=\frac{433}{20}=21.65 \).
2. \( \sum f|x-21.65|=25 \), so the mean deviation is 1.25. Hence II and III are true.

Teacher's Note:
1. Compute the mean first.

Question 13: Consider the data: marks 10, 11, 12, 14, 15 with number of students 2, 3, 8, 3, 4. I. Median is 11. II. Median is 12. III. Mean deviation about the median is 2.25. IV. Mean deviation about the median is 1.25.
(a) I and III are true
(b) I and IV are true
(c) II and III are true
(d) II and IV are true
Show Answer & Explanation

Answer: (d) II and IV are true

Explanation:
1. N = 20; the cumulative frequencies are 2, 5, 13, 16, 20. The 10th and 11th values are both 12, so the median is 12.
2. \( \sum f|x-12|=4+3+0+6+12=25 \), so the mean deviation about the median is \( \frac{25}{20}=1.25 \).

Teacher's Note:
1. Use cumulative frequencies to locate the median.

Question 14: Consider the data 6, 8, 10, 12, 14, 16, 18, 20, 22, 24. I. The variance of the data is 33. II. The standard deviation of the data is 4.74.
(a) Only Statement I is true
(b) Only Statement II is true
(c) Both statements are true
(d) Both statements are false
Show Answer & Explanation

Answer: (a) Only Statement I is true

Explanation:
1. Mean \( =15 \). Squared deviations: 81, 49, 25, 9, 1, 1, 9, 25, 49, 81; total 330. Variance \( =33 \).
2. The standard deviation is \( \sqrt{33}\approx5.74 \), not 4.74.

Teacher's Note:
1. SD is the square root of the variance.

Question 15: Statement I: the mean and variance of the first n natural numbers are \( \frac{n+1}{2} \) and \( \frac{n^2+1}{12} \). Statement II: the mean and variance of the first 10 positive multiples of 3 are 16.5 and 74.25.
(a) Only Statement I is true
(b) Only Statement II is true
(c) Both statements are true
(d) Both statements are false
Show Answer & Explanation

Answer: (b) Only Statement II is true

Explanation:
1. The variance of the first n natural numbers is \( \frac{n^2-1}{12} \), so I is false.
2. For multiples of 3: mean \( =3\cdot5.5=16.5 \) and variance \( =9\cdot\frac{99}{12}=74.25 \), so II is true.

Teacher's Note:
1. Scaling by 3 multiplies variance by 9.

Question 16: Consider the frequency distribution: class 0-10, 10-20, 20-30, 30-40, 40-50 with frequency 5, 8, 15, 16, 6. I. Mean of the data is 27. II. Mean of the data is 32. III. Variance of the data is 132. IV. Variance of the data is 164.
(a) II and IV are true
(b) I and IV are true
(c) II and III are true
(d) I and III are true
Show Answer & Explanation

Answer: (d) I and III are true

Explanation:
1. Mid-points 5, 15, 25, 35, 45: mean \( =\frac{1350}{50}=27 \).
2. \( \sum fx^2=125+1800+9375+19600+12150=43050 \), so the variance \( =\frac{43050}{50}-27^2=861-729=132 \).

Teacher's Note:
1. Use variance = mean of squares - square of mean.

Question 17: Statement I: the series having greater CV is said to be less variable than the other. Statement II: the series having lesser CV is said to be more consistent than the other.
(a) Only Statement I is true
(b) Only Statement II is true
(c) Both statements are true
(d) Both statements are false
Show Answer & Explanation

Answer: (b) Only Statement II is true

Explanation:
1. A larger coefficient of variation means more variability, so I is false.
2. A smaller CV means more consistency, so II is true.

Teacher's Note:
1. Higher CV means less consistent.

Question 18: If \( \bar x \) is the mean and \( \sigma^2 \) the variance of n observations \( x_1,\dots,x_n \), then for the observations \( ax_1,\dots,ax_n \): I. the mean is \( \bar x/a \). II. the variance is \( \sigma^2/a^2 \). III. the mean is \( a\bar x \). IV. the variance is \( a^2\sigma^2 \).
(a) I and II are true
(b) I and IV are true
(c) II and III are true
(d) III and IV are true
Show Answer & Explanation

Answer: (d) III and IV are true

Explanation:
1. Multiplying each observation by a multiplies the mean by a and the variance by \( a^2 \).
2. So III and IV are true.

Teacher's Note:
1. Scaling affects the mean linearly and the variance quadratically.

Question 19: For a distribution \( \sum(x-5)=3 \), \( \sum(x-5)^2=43 \) and the total number of items is 18. Statement I: the mean of the distribution is 4.1666. Statement II: the standard deviation of the distribution is 1.54.
(a) Only Statement I is true
(b) Only Statement II is true
(c) Both statements are true
(d) Both statements are false
Show Answer & Explanation

Answer: (b) Only Statement II is true

Explanation:
1. Mean \( =5+\frac{3}{18}=5.1666 \), so I is false.
2. Variance \( =\frac{43}{18}-\left(\frac{3}{18}\right)^2=2.3611 \), so the standard deviation is 1.54 and II is true.

Teacher's Note:
1. Shift the origin to 5.

Question 20: Consider: I. Range = maximum value - minimum value. II. Mean deviation for ungrouped data \( =\frac{\sum|x_i-\bar x|}{n} \) (about the mean) and \( \frac{\sum|x_i-M|}{n} \) (about the median M). III. Mean deviation for grouped data \( =\frac{\sum f_i|x_i-\bar x|}{N} \), where \( N=\sum f_i \). Which are true?
(a) Only I
(b) Only II
(c) Only III
(d) All of the above
Show Answer & Explanation

Answer: (d) All of the above

Explanation:
1. Each of the three statements is a standard definition.

Teacher's Note:
1. Recall the definitions.

Question 21: Consider: I. Mode can be computed from a histogram. II. Median is not independent of change of scale. III. Variance is independent of change of origin and scale. Which is/are correct?
(a) I, II and III
(b) Only II
(c) Only I and II
(d) Only I
Show Answer & Explanation

Answer: (c) Only I and II

Explanation:
1. Mode can be located from a histogram, and median changes if all observations are multiplied by a constant: I and II are true.
2. Variance is independent of change of origin but depends on the scale, so III is false.

Teacher's Note:
1. Variance changes by the square of the scale factor.

Question 22: Match: (A) mean deviation about the median for 3, 9, 5, 3, 12, 10, 18, 4, 7, 19, 21 (B) mean deviation about the median for 13, 17, 16, 14, 11, 13, 10, 16, 11, 18, 12, 17 (C) the standard deviation of n observations (D) the coefficient of variation. Column II: 1. \( \frac\sigma{\bar x}\times100 \) 2. \( \sqrt{\frac1n\sum(x_i-\bar x)^2} \) 3. 2.33 4. 5.27. Choose (A, B, C, D).
(a) 3, 4, 1, 2
(b) 4, 3, 2, 1
(c) 3, 4, 2, 1
(d) 4, 3, 1, 2
Show Answer & Explanation

Answer: (b) 4, 3, 2, 1

Explanation:
1. (A) median 9, mean deviation \( =\frac{58}{11}=5.27 \): 4.
2. (B) median 13.5, mean deviation \( =\frac{28}{12}=2.33 \): 3. (C) the SD formula is 2 and (D) the CV formula is 1.

Teacher's Note:
1. Find each median first.

Question 23: The average of 5 quantities is 6 and the average of three of them is 4. The average of the remaining two numbers is
(a) 9
(b) 6
(c) 10
(d) 5
Show Answer & Explanation

Answer: (a) 9

Explanation:
1. Total of all five: 30. Total of three: 12.
2. Remaining two sum to 18, average 9.

Teacher's Note:
1. Work with totals.

Question 24: The mean deviation from the median of the data with class intervals 0-6, 6-12, 12-18, 18-24, 24-30 and frequencies 4, 5, 3, 6, 2 is
(a) 14
(b) 10
(c) 5
(d) 7
Show Answer & Explanation

Answer: (d) 7

Explanation:
1. N = 20; cumulative frequencies 4, 9, 12, 18, 20. The median class is 12-18, with median \( 12+\frac{10-9}{3}\cdot6=14 \).
2. Mid-points 3, 9, 15, 21, 27: \( \sum f|x-14|=44+25+3+42+26=140 \), so the mean deviation \( =\frac{140}{20}=7 \).

Teacher's Note:
1. Find the median by interpolation.

Question 25: The frequency distribution is x = A, 2A, 3A, 4A, 5A, 6A with frequencies 2, 1, 1, 1, 1, 1, where A is a positive integer and the variance is 160. Then the value of A is
(a) 5
(b) 6
(c) 7
(d) 8
Show Answer & Explanation

Answer: (c) 7

Explanation:
1. N = 7. Mean \( =\frac{2A+2A+3A+4A+5A+6A}{7}=\frac{22A}{7} \).
2. \( \sum fx^2=A^2(2+4+9+16+25+36)=92A^2 \), so variance \( =\frac{92A^2}{7}-\frac{484A^2}{49}=\frac{160A^2}{49} \). Setting this equal to 160 gives \( A^2=49 \), \( A=7 \).

Teacher's Note:
1. Compute the variance in terms of A.

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Multiple Choice Questions (MCQs) for JEE Mathematics Statistics

JEE Mathematics Statistics Objective Test Questions

Review structured objective questions for JEE Mathematics Statistics. Built according to official JEE guidelines, these MCQ sets support daily revision and core concept reinforcement.

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