1. What do you mean by Python? Give the importance of Python.

Answer:

Python is a high-level, interpreted, and general-purpose programming language known for its easy-to-read syntax and versatility. It supports multiple programming paradigms such as procedural, object-oriented, and functional programming.

Importance of Python:

• Easy to learn and use due to its simple syntax.
• Large standard library and extensive third-party modules.
• Widely used in data science, web development, automation, artificial intelligence, and machine learning.
• Cross-platform compatibility.
• Strong community support and constant development.

2. Define terms: Pandas, Numpy.

Answer:

• Pandas: A powerful Python library for data manipulation and analysis. It provides data structures like DataFrame and Series for handling structured data, making it easy to clean, analyze, and visualize data.

• Numpy: Stands for Numerical Python. It is a fundamental library for numerical computations in Python, providing support for arrays, matrices, and high-level mathematical functions.

3. What do you mean by statistics? Give the major types of statistics.

Answer:

Statistics is the science of collecting, analyzing, interpreting, presenting, and organizing data.

Major types:

• Descriptive Statistics: Summarizes or describes characteristics of a data set (mean, median, mode, variance).
• Inferential Statistics: Makes inferences and predictions about a population based on a sample.

4. Explain Mean, Median, and Mode with Example.

Answer:

• Mean: Average of data. Sum all data points and divide by the number of points.

  Example: Data = 2, 3, 4
  Mean = (2 + 3 + 4)/3 = 3

• Median: Middle value when data sorted in order.

  Example: Data = 1, 3, 5 (Median = 3)

  If even number of data points, median = average of two middle numbers.

• Mode: Most frequently occurring value in the data.

  Example: Data = 2, 2, 3, 4, 4, 4
  Mode = 4

5. Define terms with example: Range, Variance, Standard Deviation

Answer:

• Range: Difference between the maximum and minimum values.

  Example: Data = 5, 8, 12
  Range = 12 - 5 = 7

• Variance: Average of the squared differences from the Mean.

  Example: Data = 1, 2, 3
  Mean = 2
  Variance = [(1-2)² + (2-2)² + (3-2)²] / 3 = (1+0+1)/3 = 0.67

• Standard Deviation: Square root of variance; measures data spread.

  Example: For above data standard deviation = √0.67 ≈ 0.82

6. What is a variable and give the different types of variables?

Answer:

A variable is a characteristic or attribute that can assume different values.

Types:

• Qualitative (Categorical): Descriptive, non-numeric (e.g., gender, color).
• Quantitative (Numerical):
  • Discrete: Countable values (e.g., number of children).
  • Continuous: Any value in a range (e.g., height, weight).

7. Explain Levels of data measurements.

Answer:

• Nominal: Categories without order (e.g., colors, gender).
• Ordinal: Categories with order but no consistent difference (e.g., ranks).
• Interval: Numeric scales with equal intervals but no true zero (e.g., temperature in Celsius).
• Ratio: Numeric with meaningful zero; allows ratio comparisons (e.g., weight, height).

8. Explain terms with example: Sample and population

Answer:

• Population: Entire set of subjects or data of interest.

  Example: All students in a university.

• Sample: A subset of the population selected for analysis.

  Example: 100 students selected randomly from the university.

9. Explain types of sampling methods.

Answer:

• Random Sampling: Every individual has an equal chance.
• Systematic Sampling: Selecting every kth individual.
• Stratified Sampling: Dividing population into strata and sampling from each.
• Cluster Sampling: Randomly selecting entire clusters/groups.
• Convenience Sampling: Selecting easily available samples (non-random).
• Quota Sampling: Selecting samples to meet quotas from subgroups.

10. Explain sampling distribution.

Answer:

Sampling distribution is the probability distribution of a statistic (e.g., mean) over many samples from the same population. It describes how the sample statistic varies from sample to sample.

11. What do you mean by Confidence interval?

Answer:

A confidence interval is a range of values, derived from sample statistics, that is likely to contain the population parameter with a certain confidence level (e.g., 95%).

12. Find the population variance and population standard deviation of the age of the children in a family of five: 16, 11, 9, 8, 1

Solution:

Step 1: Find mean
Mean = (16 + 11 + 9 + 8 + 1)/5 = 45/5 = 9

Step 2: Find squared differences
(16-9)² = 49
(11-9)² = 4
(9-9)² = 0
(8-9)² = 1
(1-9)² = 64

Step 3: Population variance (σ²)
= (49 + 4 + 0 + 1 + 64)/5 = 118 / 5 = 23.6

Step 4: Population standard deviation (σ)
= √23.6 ≈ 4.86

13. Find the population variance for the following tree heights (feet): 3, 21, 98, 203, 17, 9

Solution:

Step 1: Mean
= (3 + 21 + 98 + 203 + 17 + 9) / 6 = 351 / 6 = 58.5

Step 2: Squared differences
(3 - 58.5)² = 3090.25
(21 - 58.5)² = 1406.25
(98 - 58.5)² = 1560.25
(203 - 58.5)² = 20820.25
(17 - 58.5)² = 1712.25
(9 - 58.5)² = 2430.25

Step 3: Sum squared differences
= 3090.25 + 1406.25 + 1560.25 + 20820.25 + 1712.25 + 2430.25 = 31019.5

Step 4: Population variance
= 31019.5 / 6 = 5169.92

14. There are 45 students in a class. 5 students randomly selected with weights: 51, 38, 79, 46, 57. Calculate sample standard deviation.

Solution:

Step 1: Find sample mean
Mean = (51 + 38 + 79 + 46 + 57) / 5 = 271 / 5 = 54.2

Step 2: Squared differences
(51 - 54.2)² = 10.24
(38 - 54.2)² = 262.44
(79 - 54.2)² = 615.04
(46 - 54.2)² = 67.24
(57 - 54.2)² = 7.84

Step 3: Sum squared differences
= 10.24 + 262.44 + 615.04 + 67.24 + 7.84 = 962.8

Step 4: Sample variance (s²)
= 962.8 / (5 - 1) = 962.8 / 4 = 240.7

Step 5: Sample standard deviation (s)
= √240.7 ≈ 15.51 kg

15. Calculate sample standard deviation and sample variance for the data: 4, 7, 9, 10, 16

Solution:

Step 1: Mean
= (4 + 7 + 9 + 10 + 16) / 5 = 46 / 5 = 9.2

Step 2: Squared differences
(4 - 9.2)² = 27.04
(7 - 9.2)² = 4.84
(9 - 9.2)² = 0.04
(10 - 9.2)² = 0.64
(16 - 9.2)² = 46.24

Step 3: Sum squared differences
= 27.04 + 4.84 + 0.04 + 0.64 + 46.24 = 78.8

Step 4: Sample variance (s²)
= 78.8 / (5 - 1) = 78.8 / 4 = 19.7

Step 5: Sample standard deviation (s)
= √19.7 ≈ 4.44