Top 20 Statistics & Probability Interview Questions-Answers
Prepare for success in statistics and probability interviews with our comprehensive guide featuring the Top 20 statistics & probability Interview Questions-Answers.
1. What is statistics?
Statistics is a branch of mathematics that involves collecting, analyzing, interpreting, presenting, and organizing data. It provides methods for making inferences about the characteristics of a population based on a sample from that population.
2. What is probability?
Probability is a measure of the likelihood that a particular event will occur. It is expressed as a number between 0 and 1, with 0 indicating impossibility and 1 indicating certainty.
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3. What is the difference between population and sample?
A population is the entire group of individuals or instances about whom information is sought. A sample is a subset of the population used to make inferences about the entire population.
4. What is the Central Limit Theorem?
The Central Limit Theorem states that, under certain conditions, the distribution of the sum (or average) of a large number of independent, identically distributed random variables approaches a normal distribution, regardless of the original distribution.
5. Explain the difference between mean, median, and mode.
Mean: The average of a set of values, is calculated by adding all values and dividing by the number of values.
Median: The middle value of a dataset when it is ordered. If there is an even number of observations, the median is the average of the two middle values.
Mode: The value(s) that occur most frequently in a dataset.
6. What is the standard deviation?
Standard deviation measures the amount of variation or dispersion in a set of values. It quantifies how much the values in a dataset deviate from the mean.
7. Define correlation and covariance.
Correlation: A statistical measure that describes the extent to which two variables change together. It ranges from -1 to 1, where -1 indicates a perfect negative correlation, 1 indicates a perfect positive correlation, and 0 indicates no correlation.
Covariance: A measure of how much two random variables change together. It is the average of the product of the deviations of each value from the mean of the respective variable.
8. What are quantitative and qualitative data?
Quantitative data refers to information that can be measured and expressed with numerical values. It involves measurable quantities and is associated with numerical observations or measurements.
Types:
Discrete Data: Consists of separate, distinct values with no intermediate values (e.g., the number of students in a class).
Continuous Data: Can take any value within a given range and may have infinite possible values (e.g., height, weight).
Examples of quantitative data include age, income, height, weight, temperature, and scores on a test.
Qualitative data refers to non-numeric information that describes qualities or characteristics.
It involves categories, labels, or attributes that cannot be measured with numerical values.
Types:
Nominal Data: Represents categories without any inherent order or ranking (e.g., colors, gender, types of fruits).
Ordinal Data: Represents categories with a meaningful order or ranking but lacks a consistent interval (e.g., education levels, customer satisfaction ratings).
Examples of qualitative data include gender, hair color, city names, and the type of car a person drive
9.What are the types of sampling in Statistics?
In statistics, sampling refers to the process of selecting a subset of individuals or items from a larger population to make inferences about the entire population. There are several types of sampling methods, each with its own advantages and disadvantages. Here are some common types of sampling in statistics:
Simple Random Sampling:
Definition: Every individual or item in the population has an equal chance of being selected.
Procedure: Use random methods like lottery systems or random number generators.
Stratified Random Sampling:
Definition: The population is divided into subgroups (strata), and random samples are taken from each stratum.
Purpose: Ensures representation from each subgroup, which can be important when subgroups differ significantly.
Systematic Sampling:
Definition: Every kth individual or item is selected from a list after an initial random start.
Procedure: Determine the sampling interval (k) and randomly select a starting point.
Cluster Sampling:
Definition: The population is divided into clusters, and entire clusters are randomly selected.
Procedure: Randomly select clusters and include all individuals or items within those clusters.
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10. What do you understand by the term Normal Distribution?
A normal distribution, also known as a Gaussian distribution or bell curve, is a statistical concept that describes a specific symmetrical, bell-shaped probability distribution. It is a continuous probability distribution that is characterized by a specific set of properties:
Symmetry: The normal distribution is symmetric around its mean (average). This means that the left and right sides of the distribution are mirror images of each other.
Bell-shaped Curve: The probability density function of a normal distribution produces a bell-shaped curve. The highest point on the curve corresponds to the mean, and the curve gradually tapers off on either side.
Mean, Median, and Mode are Equal: In a normal distribution, the mean (μ), median, and mode are all equal and located at the center of the distribution.
Empirical Rule (68-95-99.7 Rule): A large percentage of the data falls within a certain number of standard deviations from the mean:
Approximately 68% of the data falls within one standard deviation.
Approximately 95% falls within two standard deviations.
Approximately 99.7% falls within three standard deviations.
11. What is a hypothesis test?
A hypothesis test is a statistical method used to make inferences about population parameters based on a sample of data. It involves formulating a null hypothesis and an alternative hypothesis, collecting data, and making a decision to either reject or fail to reject the null hypothesis.
12. Explain the p-value in hypothesis testing.
The p-value is the probability of obtaining a test statistic as extreme as, or more extreme than, the one observed in the sample data, assuming that the null hypothesis is true. A lower p-value suggests stronger evidence against the null hypothesis.
13. What is regression analysis?
Regression analysis is a statistical technique used to examine the relationship between one dependent variable and one or more independent variables. It aims to model the relationship and make predictions based on the observed data. Linear regression is a common form of regression analysis.
14. What is the difference between a parameter and a statistic?
A parameter is a numerical characteristic of a population, such as the population mean or standard deviation. A statistic is a numerical characteristic of a sample, used to estimate the corresponding population parameter.
15. What is the difference between a Type I error and a Type II error in hypothesis testing?
Type I error: Occurs when the null hypothesis is incorrectly rejected when it is actually true. It is also known as a false positive.
Type II error: Occurs when the null hypothesis is incorrectly not rejected when it is actually false. It is also known as a false negative.
16. Explain the concept of odds and odds ratio.
Odds represent the likelihood of an event occurring compared to the likelihood of it not occurring. The odds ratio compares the odds of an event in one group to the odds of the same event in another group. It is commonly used in logistic regression and case-control studies.
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17. What is a confidence interval?
A confidence interval is a range of values that is likely to include the true value of a population parameter. It provides a level of confidence, often expressed as a percentage (e.g., 95%), that the true parameter falls within the interval.
18. Define the terms sensitivity and specificity in the context of binary classification.
Sensitivity (True Positive Rate): The proportion of actual positives correctly identified by a binary classification model.
Specificity (True Negative Rate): The proportion of actual negatives correctly identified by a binary classification model.
19. How is the p-value interpreted in hypothesis testing?
Answer 3: The p-value is the probability of obtaining observed results (or more extreme) if the null hypothesis is true. A smaller p-value indicates stronger evidence against the null hypothesis. Typically, a significance level (e.g., 0.05) is chosen, and if the p-value is below this threshold, the null hypothesis is rejected.
20. What is Bayes’ Theorem?
Bayes’ Theorem is a mathematical formula that describes the probability of an event based on prior knowledge of conditions that might be related to the event. It is widely used in Bayesian statistics and machine learning.
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