Preparing for the IIT JAM Statistics exam requires strong concepts and regular practice. Many students understand the theory but still find it difficult to solve exam questions. The best way to improve problem-solving skills is to practice solved problems.

In this guide, we will look at IIT JAM Statistics solved problems from important topics such as probability, mean and variance, distributions, and correlation. These solved examples help students understand how formulas are applied in real exam questions.

Practicing solved problems is also helpful for revision because students learn the correct steps for solving questions.

Why Solved Problems are Important for IIT JAM Statistics

Solved problems help students understand how formulas are used in practice. Instead of only reading theory, students can see the step-by-step solution.

Benefits of practicing solved problems:

Improves problem-solving skills
Helps understand formulas better
Builds confidence for the exam
Makes revision easier

Students who solve many practice questions usually perform better in competitive exams.

Problem 1: Basic Probability

Question:
A box contains 5 red balls and 3 blue balls. If one ball is selected randomly, find the probability that the ball is red.

Solution

Total balls = 5 + 3 = 8
Number of red balls = 5

Using the probability formula:

P(A) = \frac{n(A)}{n(S)} $P(\text{Red}) = \frac{5}{8}$ P(Red)=85

Answer: Probability of selecting a red ball is 5/8.

Problem 2: Mean of a Data Set

Question:
Find the mean of the numbers: 5, 7, 9, 6, 8.

Solution

Mean formula: $\bar{x} = \frac{\sum x}{n}$ xˉ=n∑x

Sum of values:

5 + 7 + 9 + 6 + 8 = 35

Number of values = 5

Mean: $\bar{x} = \frac{35}{5} = 7$ xˉ=535=7

Answer: Mean = 7

Problem 3: Variance Calculation

Question:
Find the variance of the data set: 2, 4, 6, 8.

Step 1: Find the mean.

Mean: $\bar{x} = \frac{2 + 4 + 6 + 8}{4} = 5$ xˉ=42+4+6+8=5

Step 2: Use variance formula.

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

Step 3: Calculate deviations.

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

Problem 4: Binomial Distribution

Question:
If a coin is tossed 3 times, what is the probability of getting exactly 2 heads?

Solution: $P(X=k) = \binom{n}{k} p^k (1-p)^{n-k}$ P(X=k)=(kn)pk(1−p)n−k

Where

$n = 3$ n=3
$k = 2$ k=2
$p = 0.5$ p=0.5

$P(X=2) = \binom{3}{2} (0.5)^2 (0.5)^1$ P(X=2)=(23)(0.5)2(0.5)1 $= 3 \times 0.25 \times 0.5$ =3×0.25×0.5 $= 0.375$ =0.375

Answer: Probability = 0.375

Problem 5: Standard Score (Z-Score)

Question:
If the mean of a dataset is 50 and the standard deviation is 5, find the Z-score of value 60.

$z = \frac{x – \mu}{\sigma}$ 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

$x = 60$ x=60
$μ = 50$ μ=50
$σ = 5$ σ=5

$z = \frac{60 – 50}{5}$ z=560−50 $z = 2$ z=2

Answer: Z-score = 2

Problem 6: Correlation Coefficient

Question:
Two variables have covariance 20. If the standard deviations of X and Y are 4 and 5 respectively, find the correlation coefficient.

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

Substitute values: $r = \frac{20}{4 \times 5}$ r=4×520 $r = 1$ r=1

Answer: Correlation coefficient = 1

Problem 7: Normal Distribution

Question:
Find the probability that a normal variable lies within one standard deviation of the mean.

In a normal distribution:

68% of values lie within 1 standard deviation
95% lie within 2 standard deviations
99.7% lie within 3 standard deviations

Answer: Probability ≈ 0.68

Problem 8: Range of Data

Question:
Find the range of the data: 12, 18, 25, 30, 40.

Formula:

Range = Maximum − Minimum

Maximum = 40
Minimum = 12

Range: $40 – 12 = 28$ 40−12=28

Answer: Range = 28

Tips to Solve IIT JAM Statistics Problems

Students should follow a simple strategy when solving statistics questions.

1. Understand the question carefully
Read the question and identify the topic.

2. Choose the correct formula
Most statistics questions require the right formula.

3. Solve step by step
Avoid skipping steps during calculations.

4. Practice regularly
Daily practice improves speed and accuracy.

5. Revise formulas often
Knowing formulas helps solve problems faster.

Best Way to Practice IIT JAM Statistics Problems

Students can practice problems in different ways:

Solve previous year question papers
Use practice question books
Attempt mock tests
Study solved examples

Regular practice helps students become comfortable with different types of exam questions.

Why Deep Institute Helps in IIT JAM Statistics Preparation

Preparing for IIT JAM can be challenging, especially for statistics topics. Many students prefer guidance to understand concepts and solve difficult problems.

Deep Institute provides:

Structured IIT JAM Statistics study material
Practice questions with solutions
Mock tests for exam preparation
Expert faculty guidance
Doubt solving sessions

These resources help students prepare effectively for the exam.

Conclusion

Preparing for the IIT JAM Statistics exam requires strong concepts and regular practice. Studying theory alone is not enough. Students should practice many IIT JAM Statistics solved problems to understand how formulas are applied.

Solved examples help students learn the correct steps for solving questions and improve confidence before the exam. With regular practice and proper revision, students can perform well in the IIT JAM Statistics exam.

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IIT JAM Statistics Solved Problems