Preparing for the IIT JAM Statistics exam requires a strong understanding of concepts and regular practice. One of the best ways to prepare for this exam is by solving IIT JAM Statistics PYQ with solutions.

Previous year questions (PYQs) help students understand the exam pattern, difficulty level, and the type of questions asked in the exam. When students practice PYQs regularly, they improve their problem-solving skills and build confidence.

In this guide, we will discuss IIT JAM Statistics PYQ with solutions, explain important concepts, and provide practice problems that are similar to real exam questions.

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Why IIT JAM Statistics PYQ with Solutions Are Important

Many students only focus on theory books. However, solving PYQs is equally important for exam preparation.

Benefits of practicing PYQs include:

• Understanding the exam pattern
• Learning important topics
• Improving problem-solving speed
• Building confidence before the exam

Students who solve previous year questions regularly are more comfortable during the actual exam.

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Question 1: Basic Probability

Question

A bag contains 5 red balls and 5 blue balls. One ball is selected randomly. Find the probability that the ball is red.

Solution

Total number of balls = 10
Number of red balls = 5

Using the probability formula:

P(A) = \frac{n(A)}{n(S)}$$P(\text{Red}) = \frac{5}{10}$$P(Red)=105​ $$P(\text{Red}) = 0.5$$P(Red)=0.5

Answer: Probability = 0.5

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Question 2: Mean of a Dataset

Question

Find the mean of the following numbers:

10, 12, 14, 16, 18

Solution

Add all numbers:

10 + 12 + 14 + 16 + 18 = 70

Number of values = 5

Mean formula:$$\bar{x} = \frac{\sum x}{n}$$xˉ=n∑x​ $$\bar{x} = \frac{70}{5}$$xˉ=570​ $$\bar{x} = 14$$xˉ=14

Answer: Mean = 14

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Question 3: Variance

Question

Find the variance of the dataset:

2, 4, 6, 8

Step 1: Calculate the mean.$$\bar{x} = \frac{2 + 4 + 6 + 8}{4}$$xˉ=42+4+6+8​ $$\bar{x} = 5$$xˉ=5

Step 2: Apply the variance formula.

\sigma^2 = \frac{1}{N}\sum_{i=1}^{N}(x_i – \mu)^2

x	x − μ	(x − μ)²
2	-3	9
4	-1	1
6	1	1
8	3	9

Sum of squares = 20

Variance:$$\frac{20}{4} = 5$$420​=5

Answer: Variance = 5

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Question 4: Standard Deviation

Standard deviation is the square root of variance.$$\sigma = \sqrt{\sigma^2}$$σ=σ2​

Variance = 5$$\sigma = \sqrt{5}$$σ=5​

Answer: Standard deviation ≈ 2.24

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Question 5: Z-Score

Question

If mean = 50 and standard deviation = 10, find the Z-score of value 70.

$z = \frac{x – \mu}{\sigma}$z=σx−μ​

$x$x

$\mu$μ

$\sigma$σ

$z=\frac{x-\mu}{\sigma}\approx 1.2$z=σx−μ​≈1.2

$\Phi(z)\approx 88.5\%$Φ(z)≈88.5%

Where

• $x = 70$x=70
• $μ = 50$μ=50
• $σ = 10$σ=10

$$z = \frac{70 – 50}{10}$$z=1070−50​ $$z = 2$$z=2

Answer: Z-score = 2

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Question 6: Correlation Coefficient

Question

If covariance between X and Y is 12 and the standard deviations are 3 and 4, find the correlation coefficient.

Formula:$$r = \frac{Cov(X,Y)}{\sigma_x \sigma_y}$$r=σx​σy​Cov(X,Y)​

Substitute values:$$r = \frac{12}{3 \times 4}$$r=3×412​ $$r = 1$$r=1

Answer: Correlation coefficient = 1

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Question 7: Range

Question

Find the range of the dataset:

8, 10, 15, 18, 22

Range formula:

Maximum − Minimum

Maximum = 22
Minimum = 8$$Range = 22 – 8$$Range=22−8 $$Range = 14$$Range=14

Answer: Range = 14

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Question 8: Median

Question

Find the median of the dataset:

5, 7, 9, 11, 13

Since the number of values is odd, the median is the middle value.

Ordered dataset:

5, 7, 9, 11, 13

Middle value = 9

Answer: Median = 9

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Question 9: Mode

Question

Find the mode of the dataset:

2, 4, 4, 6, 7, 4, 8

The value that appears most frequently is 4.

Answer: Mode = 4

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Important Topics in IIT JAM Statistics PYQ

Based on previous exams, some topics appear more frequently.

Important topics include:

• Probability
• Random variables
• Mean, median, mode
• Variance and standard deviation
• Correlation and regression
• Probability distributions

Students should focus on these topics during preparation.

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Tips to Solve IIT JAM Statistics PYQ

Students should follow a simple strategy when solving PYQs.

Understand the Question

Read the question carefully before solving.

Identify the Topic

Find out which statistical concept is used.

Apply the Correct Formula

Using the correct formula is important for solving the question.

Practice Regularly

Regular practice improves speed and accuracy.

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Best Strategy to Practice IIT JAM Statistics PYQ

Students can improve their preparation using the following method:

• Solve at least 10–15 years of PYQs
• Try solving questions without looking at solutions
• Review mistakes carefully
• Practice again after revision

This method helps students understand the exam pattern and improve their preparation.

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Why Deep Institute Helps in IIT JAM Preparation

Preparing for IIT JAM Statistics can be challenging for many students. Guidance from experts can make preparation easier.

Deep Institute provides:

• Structured IIT JAM Statistics study material
• PYQs with solutions
• Regular mock tests
• Expert faculty guidance
• Doubt solving sessions

These resources help students prepare effectively for the exam.

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Conclusion

Preparing for the IIT JAM Statistics exam requires strong concepts and regular practice. Solving IIT JAM Statistics PYQ with solutions is one of the most effective ways to prepare for the exam.

Previous year questions help students understand the exam pattern, improve problem-solving skills, and build confidence. With regular practice and proper revision, students can perform well in the IIT JAM Statistics exam.