Preparing for the IIT JAM Statistics exam requires more than just reading theory. Many students understand formulas and concepts, but they still struggle when solving exam questions. The best way to improve your preparation is by practicing IIT JAM Statistics solved problems.

Solved problems help students see how formulas are used step by step. When you study solved examples, you learn the correct method to solve questions. This also improves speed and accuracy during the exam.

In this guide, we will look at several IIT JAM Statistics solved problems from important topics such as probability, mean, variance, correlation, and distributions.

---

Why Solved Problems Are Important for IIT JAM Statistics

Many students only read theory books. However, statistics is a practical subject. You must practice questions to understand it well.

Benefits of solved problems include:

• Understanding formulas better
• Learning step-by-step solutions
• Improving problem-solving skills
• Preparing for exam-level questions

Students who practice solved problems regularly usually perform better in competitive exams.

---

Problem 1: Probability Question

Question

A bag contains 4 white balls and 6 black balls. One ball is selected randomly. Find the probability that the ball is white.

Solution

Total balls = 4 + 6 = 10

Number of white balls = 4

Using the probability formula:

P(A) = \frac{n(A)}{n(S)}$$P(\text{White}) = \frac{4}{10}$$P(White)=104​ $$P(\text{White}) = 0.4$$P(White)=0.4

Answer: Probability = 0.4

---

Problem 2: Mean of a Data Set

Question

Find the mean of the following numbers:

10, 12, 14, 16, 18

Solution

First add all values:

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

---

Problem 3: Variance of Data

Question

Find the variance of the data set:

3, 5, 7, 9

Step 1: Find the mean.$$\bar{x} = \frac{3 + 5 + 7 + 9}{4}$$xˉ=43+5+7+9​ $$\bar{x} = 6$$xˉ=6

Step 2: Use the 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
3	-3	9
5	-1	1
7	1	1
9	3	9

Sum = 20

Variance:$$\frac{20}{4} = 5$$420​=5

Answer: Variance = 5

---

Problem 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

---

Problem 5: Binomial Distribution

Question

A coin is tossed 4 times. Find the probability of getting exactly 2 heads.

Solution:

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

Where:

• $n = 4$n=4
• $k = 2$k=2
• $p = 0.5$p=0.5

$$P(X=2) = \binom{4}{2} (0.5)^2 (0.5)^2$$P(X=2)=(24​)(0.5)2(0.5)2 $$= 6 \times 0.25 \times 0.25$$=6×0.25×0.25 $$= 0.375$$=0.375

Answer: Probability = 0.375

---

Problem 6: Z-Score Question

Question

If the mean is 70 and standard deviation is 10, find the Z-score for value 90.

$z = \frac{x – \mu}{\sigma}$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:

• $x = 90$x=90
• $μ = 70$μ=70
• $σ = 10$σ=10

$$z = \frac{90 – 70}{10}$$z=1090−70​ $$z = 2$$z=2

Answer: Z-score = 2

---

Problem 7: Correlation Coefficient

Question

If covariance between X and Y is 12, and 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

---

Problem 8: Range of Data

Question

Find the range of the data:

8, 12, 15, 20, 25

Range formula:

Maximum − Minimum

Maximum = 25
Minimum = 8

Range:$$25 – 8 = 17$$25−8=17

Answer: Range = 17

---

Problem 9: Median

Question

Find the median of the data:

5, 7, 9, 11, 13

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

Ordered data:

5, 7, 9, 11, 13

Middle value = 9

Answer: Median = 9

---

Problem 10: Mode

Question

Find the mode of the dataset:

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

The value that appears most often is 4.

Answer: Mode = 4

---

Tips to Solve IIT JAM Statistics Problems

Students should follow a simple method when solving statistics questions.

Understand the question

Read the question carefully and identify the topic.

Choose the correct formula

Many statistics questions depend on using the right formula.

Solve step by step

Do not skip calculation steps.

Practice regularly

Daily practice improves accuracy and speed.

Revise formulas

Strong formula knowledge helps solve questions faster.

---

Best Strategy to Practice Statistics Questions

Students can improve their preparation using these methods:

• Solve previous year papers
• Practice from statistics question banks
• Attempt mock tests
• Study solved examples

This helps students become familiar with exam-level questions.

---

Why Deep Institute Helps Students Prepare for IIT JAM

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

Deep Institute provides:

• Structured IIT JAM Statistics study material
• Solved practice questions
• Regular mock tests
• Expert faculty guidance
• Doubt solving sessions

These resources help students prepare in a focused and organized way.

---

Conclusion

Preparing for the IIT JAM Statistics exam requires strong concepts and regular practice. Reading theory alone is not enough. Students should practice many IIT JAM Statistics solved problems to improve their understanding.

Solved examples help students learn the correct steps for solving questions. With consistent practice, students can increase their confidence and perform well in the IIT JAM Statistics exam.