Introduction to Statistics
It is currently your data set of training until October 2023: A full-fledged module that guides participants through the complex world of probability by starting from a very solid foundation on single-event probability basic rules. The following modules will be set for more complex events and will teach advanced methods like Bayes’ theorem. This equipment prepares learners to analyze and articulate complex situations, not limited to the given environment of their understanding of probability.
The module also addresses such key probability distributions as binomial, Poisson, and normal. Effectively combining the theoretical aspects with practical applications, the module is thus likely to be equally beneficial in achieving understanding of primary principles of probability and developing the skills that make one adept at the process of data analysis. Such understanding will eventually enable them to make data-based decisions, positioning them to make grand contributions in that area. It serves as the bridge between the theory and application, hence empowering students to own the pathways through which they thread in dealing with probabilities in the world of data analysis.
Course Outcomes:
- Use Python to compute descriptive statistics.
- Determine measures of relative position, including percentile, quartile, and interquartile range.
- Determine measures of dispersion, including range, variance, and standard deviation.
- Determine measures of central tendency such as mean, median, and mode.
- Explain parameters and statistics to inferential statistics.
- Population and Sample explanation in inferential statistics.
- Difference between descriptive and inferential statistics.
PRACTICE QUIZ: TEST YOUR KNOWLEDGE: THE ROLE OF STATISTICS IN DATA SCIENCE
1. A data professional is analyzing real estate data. To estimate the mean rent of all the apartments in a large city, they calculate the mean rent of a random sample of 100 apartments. Which of the following best describes this statistical method?
- Inferential statistics (CORRECT)
- A/B testing
- Data cleaning
- Descriptive statistics
Correct: This method for data analysis is inferential statistics, which assesses information on its specific sub-population by predicting or inferring information about a larger part of the population. It enables analysts to reach conclusions, within a degree of uncertainty, which they can generalize from a smatter about a larger portion of the study population, such as through hypothesis testing, confidence intervals, and regression.
2. In statistics, a population can only include people.
- True
- False (CORRECT)
Correct: A population in statistical terms is the complete set of individuals, objects, events, or measurements sharing a similar feature and addressing inquiries in a study. For instance, this can be humans, objects, events, or whatever the specific type of relevant measurement pertaining to a research question is. The population will serve as the basis from which one draws samples for analysis.
3. The mean weight of an entire population of elephants is an example of which of the following concepts?
- Measure of dispersion
- Parameter (CORRECT)
- Data visualization
- Statistic
Correct: Example of a parameter would be mean weight of the entire population elephants. A parameter is a numerical value descriptive of a particular characteristic for a population; examples are parameters mean, median, or standard deviation. It is fixed but unknown, however, because fixing the populace part is impractical: It is equal to a certain value, which is usually unknown because it has to do with the whole population, which is mostly impractical to measure. Instead, a statistic is the processed derived from an element sample meant to estimate the corresponding parameter of a population.
PRACTICE QUIZ: TEST YOUR KNOWLEDGE: DESCRIPTIVE STATISTICS
1. A data professional is analyzing sales data for an online store. The most frequently occurring value in the dataset is $150. What term is used to describe this value?
- Mode (CORRECT)
- Interquartile range
- Median
- Variance
Correct!
2. What do measures of dispersion represent?
- The relative position of the values in a dataset
- The center of a dataset
- The total number of values in a dataset
- The spread of a dataset (CORRECT)
Correct: Measures of dispersion represent the spread of a dataset, or how spread out the values are from the center.
3. Which of the following descriptive statistics are measures of position? Select all that apply.
- Standard deviation
- Mean
- Percentile (CORRECT)
- Quartile (CORRECT)
Correct: There are different measures of position such as quartiles and percentiles. A quartile divides a data set into 4 equal parts and describes 25 percent of values in the distribution. The three quartiles are the first quartile (Q1), second quartile (Q2, which is the median), and third quartile (Q3).
Correct: Position measures cover quartiles and percentiles. Each quartile in a data set divides the data into four equal parts, with each quartile of the data measuring 25%. The first quartile (Q1), the second quartile (Q2) or median (50th percentile), and the third quartile (Q3) mark the 75th percentile.-mark the 25th percentile.
PRACTICE QUIZ: TEST YOUR KNOWLEDGE: CALCULATE STATISTICS WITH PYTHON
1. What two Python functions can you use to compute the range of your dataset?
- mean() and min()
- max() and std()
- max() and min() (CORRECT)
- max() and median()
Correct: The difference between maximum and minimum determines the extent of a dataset. The function max() gives output in the form of the maximum value of the set. Whereas min() function yields the minimum value in the set.
2. What Python function can data professionals use to compute the mean, median, and standard deviation all at once?
- std()
- median()
- mean()
- describe() (CORRECT)
Correct: Incorporating the describe() function, data experts may now compute all the key statistical measures for a given dataset: mean, median, standard deviation, minimum and maximum values, including the quartiles (25th, 50th, and 75th percentiles) at once. This function provides a quick overview of the central tendency, spread, and distribution of the data.
QUIZ: MODULE 1 CHALLENGE
1. A community college wants to improve student engagement with their new class schedule. They send a text alert to all students with a link to the same webpage. But half of the students get a text with information about the professors, and half get a text with information about newly available class times. What does this scenario describe?
- Time series analysis
- Hypothesis testing
- Regression analysis
- A/B testing (CORRECT)
Correct!
2. Which of the following statements correctly describe key elements of inferential statistics? Select all that apply.
- Sample size has minimal impact on the validity of test results.
- A statistical population may refer to people, objects, or events. (CORRECT)
- Data professionals use inferential statistics to predict behaviors. (CORRECT)
- A sample is a subset of the larger population. (CORRECT)
3. A data team at a high-tech manufacturer wants to better understand customer purchases of webcams over the past five years. Their dataset contains about 3.5 million rows of data about different customers and webcam products. The data team uses summary statistics to better understand the data. What does this scenario describe?
- Inferential statistics
- Statistical significance
- Confidence intervals
- Descriptive statistics (CORRECT)
Correct!
4. Fill in the blank: A _____ is a characteristic of a population.
- sample
- parameter (CORRECT)
- measure
- range
Correct!
5. A data professional working at an online store analyzes data for a monthly business intelligence report. They calculate the average time customers spend on the store’s website. What descriptive statistic are they using?
- Range
- Mean (CORRECT)
- Mode
- Standard deviation
Correct!
6. A data professional works with the following dataset: 2, 2, 4, 7, 10. What is the mean of the dataset?
- 4
- 5 (CORRECT)
- 10
- 2
Correct!
7. What concept best describes the standard deviation, variance, and range?
- Measures of central tendency
- Measures of frequency
- Measures of dispersion (CORRECT)
- Measures of position
Correct!
8. A data professional is analyzing wind speed data. Their dataset includes daily speeds in miles per hour over six months: 1, 8, 9, 14, 22, 28, 35, 46, 55, 60, 71. What is the range of their dataset?
- 31.7
- 28
- 70 (CORRECT)
- 349
Correct!
9. A data professional is analyzing data about annual work income in dollars. They divide the data into quartiles: Q1 = $40,000, Q2 = $55,000, Q3 = $70,000. What percentage of the values in their dataset are above $70,000?
- 5%
- 50%
- 25% (CORRECT)
- 75%
Correct!
10. If you apply the describe() function to numerical data, the results will include which of the following descriptive statistics? Select all that apply.
- Range
- Median (CORRECT)
- Mean (CORRECT)
- Standard deviation (CORRECT)
Correct!
11. A grocery delivery business wants to improve customer response rates for their company’s monthly postcard mailer. They send a postcard with the same information to all customers. But half of the customers get a headline about faster delivery speeds, and half get a headline about more delivery drivers available in their area. What does this scenario describe?
- Regression analysis
- Hypothesis testing
- Time series analysis
- A/B testing (CORRECT)
Correct!
12. Fill in the blank: A characteristic of a _____ is a parameter.
- sample
- measure
- range
- population (CORRECT)
Correct!
13. A data analytics team collects responses from a customer satisfaction survey that asked customers to rate their experience from 1 to 10. The analytics team arranges the values in the dataset from worst (1) to best (10). Then, they identify the middle value. What descriptive statistic are they using?
- Mode
- Minimum
- Mean
- Median (CORRECT)
Correct!
14. A data professional works with the following dataset: 2, 2, 4, 7, 10. What is the median of the dataset?
- 5
- 7
- 2
- 4 (CORRECT)
Correct!
15. A data professional is analyzing weather data. Their dataset includes daily rainfall in inches for the previous five days: 1, 2.4, 3.2, 5, 2.8. What is the range of their dataset?
- 3.2
- 5
- 2.4
- 4 (CORRECT)
Correct!
16. A data professional is analyzing data about annual work income in dollars. They divide the data into quartiles: Q1 = $40,000, Q2 = $55,000, Q3 = $70,000. What value is the 50th percentile of their dataset?
- $30,000
- $40,000
- $55,000 (CORRECT)
- $70,000
Correct!
17. Which of the following statements correctly describes key elements of inferential statistics? Select all that apply.
- Sample size has minimal effect on the validity of test results.
- Data professionals use inferential statistics to predict behaviors. (CORRECT)
- The dataset that a sample is drawn from is called the population. (CORRECT)
- A sample can be used to draw conclusions about an entire population. (CORRECT)
Correct!
18. A data professional working for a water conservancy researches household water usage in a large city. Their dataset contains about 800,000 rows of data capturing how much water each household uses in a month. The data professional creates visualizations to quickly understand the data and create a summary for stakeholders. What does this scenario describe?
- Statistical significance
- Confidence intervals
- Inferential statistics Descriptive statistics (CORRECT)
Correct!
19. A company conducts an employee satisfaction survey. Employees rate their work experience as unacceptable, average, good, or excellent. The most frequently occurring value in the survey is excellent. What descriptive statistics concept best describes this value?
- Standard deviation
- Mode (CORRECT)
- Median
- Mean
Correct!
20. Which of the following descriptive statistics are measures of dispersion? Select all that apply.
- Percentile
- Standard deviation (CORRECT)
- Variance (CORRECT)
- Range (CORRECT)
Correct!
21. A data professional is analyzing data about annual work income in dollars. They divide the data into quartiles: Q1 = $40,000, Q2 = $55,000, Q3 = $70,000. What is the interquartile range, or IQR, of their dataset?
- $15,000
- $30,000 (CORRECT)
- $40,000
- $55,000
Correct!
22. A data team at a car dealership wants to improve open rates for their company’s weekly email campaign. They send two versions of the weekly email. Half of the customers get a subject line about new car colors, and half get a subject line about new car interiors. What does this scenario describe?
- Hypothesis testing
- Regression analysis
- A/B testing (CORRECT)
- Time series analysis
Correct!
23. Fill in the blank: A _____ is a characteristic of a sample.
- range
- parameter
- measure
- statistic (CORRECT)
Correct!
24. What do measures of dispersion, such as range and standard deviation, help a data professional understand about their data?
- Minimum value
- Center
- Spread (CORRECT)
- Maximum value
Correct!
25. A data team at a landscaping company investigates the most weather-resistant tree species in Canada. Their dataset contains more than 1 million rows of data about different trees. The data team creates a table to better understand what the data reveals. What does this scenario describe?
- Descriptive statistics (CORRECT)
- Inferential statistics
- Statistical significance
- Confidence intervals
Correct!
26. A data professional works with the following dataset: 2, 2, 4, 7, 10. What is the mode of the dataset?
- 10
- 2 (CORRECT)
- 7
- 4
Correct!
27. A data professional is analyzing tomato growth data. Their dataset includes the circumference of tomatoes in millimeters: 40, 49, 50, 52, 66.3, 77.5, 78, 80. What is the range of their dataset?
- 51
- 500.3
- 40 (CORRECT)
- 62.5
Correct!
28. A data professional is analyzing data about the employees of a corporation. They want to compute the average age of all employees in the dataset. What Python functions can they use? Select all that apply.
- max()
- std()
- mean() (CORRECT)
- describe() (CORRECT)
Correct!
29. Which of the following statements correctly describe key elements of inferential statistics? Select all that apply.
- Inferential statistics is the process of selecting a subset of data from a population.
- Sampling is the process of selecting a subset of data from a population. (CORRECT)
- A population includes every possible element to be measured. (CORRECT)
- Before conducting a test, data professionals choose the sample size. (CORRECT)
Correct!
30. If you apply the describe() function to categorical data, the results will include which of the following descriptive statistics?
- Median
- Mode (CORRECT)
- Mean
- Standard deviation
Correct!
31. Descriptive statistics enable data professionals to summarize the main features of a dataset.
- True (CORRECT)
- False
Correct: It helps in summarizing and highlighting the main features of the data and gives to those who perform their functions clear overview about its structure and characteristics. It reduces large amounts of data into meaningful metrics to understand them quickly.
32. Fill in the blank: The _____ is the average value in a dataset.
- mode
- sample
- mean (CORRECT)
- median
Correct: The mean is essentially the average of all the data points in a dataset and mathematically defined as summation of all the values followed by division through the number of values in the dataset. It serves as a measure of central tendency that specifies the typical or expected value indicated by the data.
33. What descriptive statistic measures the spread of the values from the mean of a dataset?
- Mode
- Median
- Range
- Standard deviation (CORRECT)
Correct:Standard deviations inform us about the distribution or dispersion of the values relative to the mean. It gives an idea of how the points differ or deviate from the mean value. Lower standard deviation means the values are closer to the mean, and high standard deviation means that the values vary more widely.
34. What measure of position divides the values in a dataset into four equal parts?
- Decile
- Quintile
- Quartile (CORRECT)
- Percentile
Correct: A quartile divides the members of a dataset into four equal parts to better study the distribution of the data collected by it.
CONCLUSION – probability
This probability will offer the participants a very comprehensive and organized journey through both principles and advanced techniques in probability theory. Foundations will be laid with elementary single-event probabilities, gradually proceeding to complex ones, such as bayes’ theorem. Not a very detailed analysis will be performed on some of the most important probability distributions, such as the binomial, Poisson, and normal distributions, enabling the participant to start using the analytical tools needed to understand various data patterns.
This integration of theory and practice states that the knowledge built was at a strong foundation and developed practical skills essential in data analysis. The students can analyze a data scenario, make data-driven decisions, and contribute to working in a bigger field of data analysis. This module showcases a whole-broad overview that it takes toward getting familiarized with probability regarding real-world application, thus placing the learners prepared to use these concepts in actual contexts.