Practice Questions on Data Handling

Data handling refers to the process of managing and manipulating data. In this article, we will learn how to solve questions based on data handling. This article provides practice questions based on data handling.

Following are some important formulas helpful in solving Data Handling questions

Measures of Central Tendency

• Mean (μ) = (Σx)/n
• Median: Middle value in a sorted dataset or (n + 1)/2th value if n is odd
• Mode: Most frequently occurring value in a dataset

Measures of Dispersion

• Range = Maximum value – Minimum value
• Variance (σ²) = Σ((x – μ)²)/n
• Standard Deviation (σ) = √Variance

Correlation

• Pearson correlation coefficient (r) = Σ((x – x̄)(y – ȳ)) / √(Σ(x – x̄)² × Σ(y – ȳ)²)

Regression

• Linear Regression: y = mx + c (where m is the slope and c is the intercept)
• Slope (m) = Σ((x – x̄)(y – ȳ)) / Σ(x – x̄)²
• Intercept (c) = ȳ – m×x̄

Hypothesis Testing

• Z-test: Z = (X̄ – μ) / (σ / √n), where X̄ is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size
• t-test: t = (X̄ – μ) / (s / √n), where s is the sample standard deviation

Q1. The following dataset represents the scores obtained by students in a mathematics exam: [75, 80, 85, 90, 85, 70, 80, 85, 90, 95]. Calculate the mean, median, and mode of the dataset.

Solution:

Mean = (75 + 80 + 85 + 90 + 85 + 70 + 80 + 85 + 90 + 95) / 10 = 855 / 10 = 85.5

Median = (85 + 85) / 2 = 85

Mode = 85

Q2. Compute the range, variance, and standard deviation for the following dataset: [10, 15, 20, 25, 30]

Solution:

Range = Maximum value – Minimum value = 30 – 10 = 20

Mean = (10 + 15 + 20 + 25 + 30) / 5 = 100 / 5 = 20

Variance = [(10 – 20)² + (15 – 20)² + (20 – 20)² + (25 – 20)² + (30 – 20)²] / 5

= (100 + 25 + 0 + 25 + 100) / 5 = 250 / 5 = 50

Standard Deviation = √Variance = √50 ≈ 7.07

Q3. Calculate the Pearson correlation coefficient (r) for the following dataset:

X: [10, 15, 20, 25, 30]

Y: [20, 25, 30, 35, 40]

Solution:

Mean of X = (10 + 15 + 20 + 25 + 30) / 5 = 100 / 5 = 20

Mean of Y = (20 + 25 + 30 + 35 + 40) / 5 = 150 / 5 = 30

Σ((x – x̄)(y – ȳ)) = (10 – 20)(20 – 30) + (15 – 20)(25 – 30) + (20 – 20)(30 – 30) + (25 – 20)(35 – 30) + (30 – 20)(40 – 30)

= (-10 × -10) + (-5 × -5) + (0 × 0) + (5 × 5) + (10 × 10)

= 100 + 25 + 0 + 25 + 100 = 250

Σ(x – x̄)² = (10 – 20)² + (15 – 20)² + (20 – 20)² + (25 – 20)² + (30 – 20)²

= 100 + 25 + 0 + 25 + 100 = 250

Σ(y – ȳ)² = (20 – 30)² + (25 – 30)² + (30 – 30)² + (35 – 30)² + (40 – 30)²

= 100 + 25 + 0 + 25 + 100 = 250

r = Σ((x – x̄)(y – ȳ)) / √(Σ(x – x̄)² × Σ(y – ȳ)²)

= 250 / √(250 × 250) = 250 / 250 = 1 ×

Q4. Perform a t-test for the given dataset to test the hypothesis that the mean is 20:

Dataset: [18, 19, 21, 22, 20, 23, 17, 20, 19, 20]

(Assuming a significance level of 0.05)

Solution:

Mean = (18 + 19 + 21 + 22 + 20 + 23 + 17 + 20 + 19 + 20) / 10 = 199 / 10 = 19.9

Standard Deviation = √[(Σ(x – x̄)²) / (n – 1)] = √[(16.9 + 9.6 + 0.1 + 4.1 + 0.1 + 9.6 + 5.6 + 0.1 + 0.1 + 0.1) / 9]

= √(45.2 / 9) = √5.022 ≈ 2.24

t = (X̄ – μ) / (s / √n) = (19.9 – 20) / (2.24 / √10) ≈ -0.224

Degrees of Freedom (df) = n – 1 = 10 – 1 = 9

Critical t-value for df = 9 at α = 0.05 (two-tailed) is approximately ±2.262

Since |-0.224| < 2.262, we fail to reject the null hypothesis.

Q5. The heights (in inches) of a sample of 5 students are as follows: 65, 68, 70, 63, 72. Calculate the mean height of the students.

Solution :

Mean = (65 + 68 + 70 + 63 + 72) / 5

Mean = 338 / 5

Mean = 67.6 inches

Q6. Calculate the variance of the following dataset: 5, 8, 10, 12, 15.

Solution :

Mean = (5 + 8 + 10 + 12 + 15) / 5

Mean = 50 / 5

Mean = 10.

Now, calculate the squared deviations from the mean:

(5 – 10)² = 25

(8 – 10)² = 4

(10 – 10)² = 0

(12 – 10)² = 4

(15 – 10)² = 25

Variance = (25 + 4 + 0 + 4 + 25) / 5

Variance = 58 / 5

Variance = 11.6.

Q7. What is the correlation coefficient if the covariance between two variables X and Y is 50, the standard deviation of X is 5, and the standard deviation of Y is 10?

Solution :

Correlation coefficient (r) = Covariance / (Standard deviation of X × Standard deviation of Y)

r = 50 / (5 × 10)

r = 50 / 50

r = 1

Q8. Perform a t-test with the following data: sample mean = 65, population mean = 60, sample standard deviation = 8, sample size = 25. Assume a significance level of 0.05.

Solution:

t = (X̄ – μ) / (s / √n)

t = (65 – 60) / (8 / √25)

t = 5 / (8 / 5)

t = 5 / 1.6

t ≈ 3.125.

With a significance level of 0.05 and 24 degrees of freedom (n – 1), the critical t-value is approximately 2.064. Since 3.125 > 2.064, we reject the null hypothesis.

Q9. Calculate the median of the following dataset: 12, 15, 18, 20, 22, 25, 28, 30.

Solution:

Since there are 8 data points, the median is the average of the 4th and 5th terms.

Median = (20 + 22) / 2

Median = 21.

Question :

Find the range of the following dataset: 10, 15, 20, 25, 30.

Solution :

Range = Maximum value – Minimum value

Range = 30 – 10

Range = 20

Q1. Calculate the mode of the following dataset: 12, 15, 18, 20, 22, 25, 28, 30.

Q2. Find the standard deviation of the following dataset: 5, 8, 10, 12, 15.

Q3. Given the following dataset: 18, 20, 22, 24, 26, 28, 30, 32. Perform a Z-test with a sample mean of 25, population mean of 22, sample standard deviation of 4, and a sample size of 20. Use a significance level of 0.05.

Q4. Create a scatter plot for the following dataset:

X: 10, 15, 20, 25, 30

Y: 5, 8, 12, 18, 22

Q5. Explain the difference between descriptive and inferential statistics. Give examples of each.

Q6. Discuss the ethical considerations in handling data, especially in the context of data privacy and bias.

Q7. What are the advantages and disadvantages of using surveys as a method of data collection?

Q8. Calculate the Pearson correlation coefficient for the following dataset:

X: 25, 30, 35, 40, 45

Y: 12, 15, 20, 25, 30

Q9. Explain the concept of data preprocessing and discuss its significance in data analysis.

Q10. What are some common data visualization tools and techniques used in data handling? Provide examples of each.

What is data handling, and why is it important?

Data handling involves managing, organizing, analyzing, and interpreting data to extract meaningful insights and make informed decisions. It is important because it allows organizations to leverage the vast amounts of data they collect to improve processes, understand customer behavior, drive innovation, and gain a competitive edge.

What are the main steps involved in data handling?

The main steps in data handling include data collection, data cleaning and preprocessing, data storage, data analysis, data visualization, and data interpretation. Each step plays a crucial role in ensuring the accuracy, reliability, and usefulness of the data.

What are some common challenges in data handling?

Common challenges in data handling include dealing with missing or incomplete data, ensuring data quality and accuracy, protecting data security and privacy, managing large volumes of data (big data), integrating data from diverse sources, and complying with regulations and standards related to data handling.

How is data visualization helpful in data handling?

Data visualization involves presenting data in visual formats such as charts, graphs, and maps to facilitate understanding and interpretation. It helps identify patterns, trends, and relationships in the data, communicate findings effectively to stakeholders, and support decision-making processes.

How can organizations address data bias in their data handling processes?

Organizations can address data bias by being aware of biases inherent in their data sources and analysis methods, diversifying data sources to reduce bias, implementing algorithms and models that mitigate bias, regularly evaluating and auditing their data handling processes for bias, and fostering a culture of diversity and inclusion within the organization