Definition
A statistic is a numerical characteristic or measure derived from a subset (sample) of a more extensive set of data, namely the population. It is crucial in understanding various aspects of the data by summarizing, analyzing, and making inferences about the population from which the sample is drawn.
Statistics allow for the estimation of population parameters (like mean, median, and mode) and are pivotal in diverse fields, including economics, biology, engineering, and social sciences. Examples of commonly used statistics include sample mean, sample variance, and sample proportion.
Examples
- Sample Mean: Calculated as the sum of all sample values divided by the number of values in the sample. It’s an estimate of the population mean.
- Sample Variance: Measures the dispersion or variability in the sample data. It is calculated as the sum of the squared differences between each sample value and the sample mean, divided by the number of sample values minus one.
- Sample Proportion: Represents the proportion of a particular attribute in the sample, which can be used to estimate the population proportion.
Frequently Asked Questions
What is the difference between a statistic and a parameter?
A statistic is a measurable characteristic of a sample, while a parameter is a measurable characteristic of a population. Statistics are used to estimate parameters.
How are statistics helpful?
Statistics play a crucial role in data analysis by summarizing large sets of data into understandable measures, helping in making informed decisions, conducting hypothesis tests, and generating predictive models.
What are the common types of statistics?
The common types of statistics include measures of central tendency (mean, median, mode), measures of dispersion (variance, standard deviation, range), and measures of association (correlation, regression).
Can statistics be used to make predictions?
Yes, statistics can be used to make predictions about future events or population characteristics based on sample data and probabilistic models.
Population: The entire group being studied, from which a sample is drawn.
Sample: A subset of the population used to infer information about the population.
Parameter: A numerical characteristic of a population, such as mean or variance.
Inferential Statistics: Techniques used to make generalizations and predictions about a population based on a sample.
Descriptive Statistics: Methods used to describe and summarize data, including statistical measures like mean and variance.
Online References
- Investopedia: Statistics and Examples
- Wikipedia: Statistic
Suggested Books for Further Studies
- “Introductory Statistics” by Sheldon M. Ross
- “The Elements of Statistical Learning” by Trevor Hastie, Robert Tibshirani, and Jerome Friedman
- “Statistical Methods” by Rudolf J. Freund, William J. Wilson, and Paul S. Tardiff
- “Applied Multivariate Statistical Analysis” by Richard A. Johnson and Dean W. Wichern
- “An Introduction to Statistical Learning” by Gareth James, Daniela Witten, Trevor Hastie, and Robert Tibshirani
Fundamentals of Statistic: Statistics Basics Quiz
### What is a statistic compared to a parameter?
- [x] A measurement taken from a sample.
- [ ] A measurement taken from a population.
- [ ] A theoretical concept without practical application.
- [ ] An exact number representing a population.
> **Explanation:** A statistic is a measurement derived from a sample, as opposed to a parameter, which describes a characteristic of the entire population.
### How can the sample mean be described?
- [x] Sum of all sample values divided by the number of values in the sample.
- [ ] Sum of all population values divided by the number of values in the population.
- [ ] The most frequent value in a set of data.
- [ ] The middle value of a data set when arranged in order.
> **Explanation:** The sample mean is calculated by summing all values in the sample and then dividing by the number of values, providing an estimate of the population mean.
### What does sample variance measure?
- [ ] The mean of the population data.
- [x] The dispersion or spread of sample data.
- [ ] The most common value in a data set.
- [ ] The theoretical distribution shape of a data set.
> **Explanation:** Sample variance measures the dispersion or variability in a sample by considering the squared differences between each sample value and the sample mean.
### What is the first step in calculating sample proportion?
- [ ] Square all values.
- [ ] Subtract the sample mean from all values.
- [x] Count the number of occurrences of the attribute of interest.
- [ ] Calculate the sample variance.
> **Explanation:** The initial step in calculating the sample proportion is to count the occurrences of the attribute of interest within the sample.
### Which type of statistics would be used to make predictions about future events?
- [x] Inferential Statistics
- [ ] Descriptive Statistics
- [ ] Analytical Statistics
- [ ] Experimental Statistics
> **Explanation:** Inferential statistics involve methods that allow for making predictions and drawing conclusions about a population based on sample data.
### What does descriptive statistics generally include?
- [ ] Hypothesis tests and estimations.
- [x] Measures of central tendency, dispersion, and graphical displays.
- [ ] Simple random sampling techniques.
- [ ] Experimental designs and controls.
> **Explanation:** Descriptive statistics include measures of central tendency, dispersion, and methods to summarize and visualize data.
### In the context of statistics, what is a 'population'?
- [ ] A sample derived from another sample.
- [ ] An artificial subset of data.
- [x] The entire group of individuals or entities being studied.
- [ ] A numerical measurement from a sample.
> **Explanation:** A population is the whole group being studied in a statistical analysis, from which samples are drawn to make inferences.
### Why is sampling important in statistical studies?
- [ ] Because it's cheaper than studying the whole population.
- [x] It allows for estimating characteristics of the population from a sample.
- [ ] It eliminates errors in data collection.
- [ ] It ensures certainty in results.
> **Explanation:** Sampling is crucial because it enables the estimation of population characteristics based on data from a smaller, more manageable subset.
### What is the role of a sample in statistics?
- [x] To provide a manageable subset of data from which inferences about a population can be made.
- [ ] To provide infinite data points.
- [ ] To serve as the entire focus of a study.
- [ ] To replicate the entire population.
> **Explanation:** A sample furnishes a smaller, manageable set of data which researchers use to infer properties about the broader population.
### Which method is used to summarize large data sets into understandable terms?
- [ ] Inferential statistics.
- [x] Descriptive statistics.
- [ ] Parametric statistics.
- [ ] Predictive analytics.
> **Explanation:** Descriptive statistics are employed to summarize and present large data sets in a simplified and understandable manner.
Thank you for delving into the extensive world of statistics, refining your understanding and tackling our comprehensive quiz questions. Continue exploring and refining your knowledge in this fascinating field!
