JEE (Main) Mathematics - Statistics and Probability Multiple Choice Questions

Which of the following measures is used to calculate the central tendency of grouped data?
a) Range
b) Mode
c) Mean
d) Median
Answer: c) Mean
For a set of data, the mode is 10 and the median is 12. Which of the following is a possible characteristic of this data?
a) The distribution is symmetric
b) The distribution is skewed right
c) The distribution is skewed left
d) The mean is equal to 12
Answer: b) The distribution is skewed right
Which of the following is the correct formula for variance in a frequency distribution?
a) \( \sigma^2 = \frac{\sum (X - \mu)^2}{n} \)
b) \( \sigma^2 = \frac{\sum f (X - \mu)^2}{n} \)
c) \( \sigma^2 = \frac{\sum (X - \mu)^2}{n-1} \)
d) \( \sigma^2 = \sum (X - \mu) \)
Answer: b) \( \sigma^2 = \frac{\sum f (X - \mu)^2}{n} \)
If the mean of a set of data is 20, and the sum of squares of deviations from the mean is 400, what is the variance of the data?
a) 10
b) 20
c) 40
d) 50
Answer: c) 40
The probability of event A occurring is \( P(A) = 0.6 \), and the probability of event B occurring is \( P(B) = 0.4 \). If A and B are independent, what is the probability of both A and B occurring?
a) 0.24
b) 0.10
c) 0.20
d) 0.60
Answer: a) 0.24
If the mean of the data set {5, 7, 9, 10, 12} is 8.6, what is the value of the median?
a) 9
b) 8
c) 10
d) 7
Answer: a) 9
The variance of a data set is 16. What is the standard deviation of the data?
a) 16
b) 8
c) 4
d) 2
Answer: c) 4
In a probability distribution, if the sum of the probabilities of all outcomes is less than 1, then the distribution is:
a) Valid
b) Inconsistent
c) Impossible
d) Invalid
Answer: d) Invalid
Which of the following is true according to Bayes’ Theorem?
a) \( P(A|B) = \frac{P(A \cap B)}{P(B)} \)
b) \( P(A|B) = \frac{P(B|A) \cdot P(A)}{P(B)} \)
c) \( P(A \cap B) = P(A) \cdot P(B) \)
d) \( P(A|B) = P(A) + P(B) \)
Answer: b) \( P(A|B) = \frac{P(B|A) \cdot P(A)}{P(B)} \)
A die is rolled once. What is the probability of getting a number greater than 4?
a) \( \frac{1}{3} \)
b) \( \frac{1}{2} \)
c) \( \frac{1}{6} \)
d) \( \frac{5}{6} \)
Answer: a) \( \frac{1}{3} \)
In a class of 40 students, 25 students passed an exam. What is the probability that a randomly selected student passed the exam?
a) \( \frac{1}{2} \)
b) \( \frac{25}{40} \)
c) \( \frac{1}{5} \)
d) \( \frac{2}{5} \)
Answer: b) \( \frac{25}{40} \)
What is the probability of drawing a king from a deck of 52 cards?
a) \( \frac{1}{13} \)
b) \( \frac{1}{26} \)
c) \( \frac{1}{52} \)
d) \( \frac{4}{52} \)
Answer: d) \( \frac{4}{52} \)
The probability of event A is \( P(A) = 0.7 \), and the probability of event B is \( P(B) = 0.6 \). If events A and B are independent, what is the probability of event A or event B occurring?
a) \( 0.72 \)
b) \( 1.3 \)
c) \( 0.88 \)
d) \( 1.0 \)
Answer: c) \( 0.88 \)
In a box containing 5 red balls, 3 green balls, and 2 blue balls, what is the probability of drawing a green ball?
a) \( \frac{3}{10} \)
b) \( \frac{2}{10} \)
c) \( \frac{1}{5} \)
d) \( \frac{3}{5} \)
Answer: a) \( \frac{3}{10} \)
Which of the following is the correct formula for the mean deviation for ungrouped data?
a) \( \frac{\sum |X - \mu|}{n} \)
b) \( \frac{\sum |X - M|}{n} \)
c) \( \frac{\sum |X - \mu|}{n-1} \)
d) \( \frac{\sum |X - X_{median}|}{n} \)
Answer: a) \( \frac{\sum |X - \mu|}{n} \)

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JEE (Main) Mathematics - Statistics and Probability Multiple Choice Questions

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