JEE (Main) Mathematics - Statistics and Probability MCQs (16 to 30)

16. The range of the data 10, 20, 30, 40, 50 is:

a) 40

b) 30

c) 20

d) 10

Answer: a) 40

17. The mean of the following data: 5, 10, 15, 20, 25 is:

a) 10

b) 12

c) 15

d) 20

Answer: c) 15

18. The mode of the grouped frequency distribution is given by the formula:

a) \( L + \frac{(f_1 - f_0)}{(2f_1 - f_0 - f_2)} \times h \)

b) \( L + \frac{(f_0 - f_1)}{(f_0 - f_1 + f_2)} \times h \)

c) \( L + \frac{(f_2 - f_1)}{(f_2 + f_1 - f_0)} \times h \)

d) \( L + \frac{(f_1 - f_2)}{(f_1 + f_2 - f_0)} \times h \)

Answer: a) \( L + \frac{(f_1 - f_0)}{(2f_1 - f_0 - f_2)} \times h \)

19. In a grouped frequency distribution, the mean is calculated using the formula:

a) \( \sum fx / \sum f \)

b) \( \sum x / \sum f \)

c) \( \sum f / \sum x \)

d) \( \sum f \times x / \sum f \)

Answer: a) \( \sum fx / \sum f \)

20. The quartile deviation is defined as:

a) \( QD = Q_3 - Q_1 \)

b) \( QD = (Q_3 - Q_1) / 2 \)

c) \( QD = (Q_1 + Q_3) / 2 \)

d) \( QD = (Q_3 - Q_1) \times 2 \)

Answer: b) \( QD = (Q_3 - Q_1) / 2 \)

21. The standard deviation of the set of numbers 1, 3, 5, 7, 9 is:

a) 2

b) 2.58

c) 3

d) 4

Answer: b) 2.58

22. If the mean of a data set is 50 and the variance is 25, what is the standard deviation?

a) 5

b) 10

c) 25

d) 2

Answer: a) 5

23. The median of the data set 5, 12, 8, 14, 7 is:

a) 7

b) 8

c) 12

d) 10

Answer: b) 8

24. The mode of the data set 3, 3, 5, 7, 9, 5, 5 is:

a) 3

b) 5

c) 7

d) 9

Answer: b) 5

25. The arithmetic mean of a set of observations is 30. If the sum of the observations is 150, then the number of observations is:

a) 4

b) 5

c) 6

d) 7

Answer: b) 5

26. The mean of the following data: 6, 10, 14, 20, 24 is:

a) 12

b) 14

c) 15

d) 16

Answer: b) 14

27. The variance of the data 4, 6, 8, 10, 12 is:

a) 8

b) 10

c) 9

d) 7

Answer: c) 9

28. The median of the data 8, 12, 15, 20, 25 is:

a) 15

b) 12

c) 13

d) 14

Answer: a) 15

29. In a frequency distribution, if the sum of frequencies is 60, and the sum of the product of the frequencies and their corresponding class marks is 1800, the mean is:

a) 30

b) 35

c) 40

d) 45

Answer: c) 40

30. The sum of deviations of a data set from the mean is always:

a) Zero

b) Positive

c) Negative

d) Equal to the variance

Answer: a) Zero