Indicate whether each of the following statements is true or false:
a. Statistics is the science of collecting, organizing, analyzing, interpreting, and presenting data.
b. A statistic is a single measure, reported as a number, used to summarize a sample data set.
c. Descriptive statistics refers to generalizing from a sample to a population, estimating unknown parameters, drawing conclusions, and making decisions.
d. One of the advantages of censuses is that they provide up-to-date data.
e. Inferential statistics refers to the collection, organization, presentation, and summary of data, either by using charts and graphs or through numerical summaries.
The Correct and E xplanation is:
Here are the correct responses with explanations for each statement:
a. Statistics is the science of collecting, organizing, analyzing, interpreting, and presenting data.
✅ True
This is the correct definition of statistics. Statistics is a branch of mathematics focused on gathering and interpreting data to uncover patterns and trends. It encompasses all aspects of the data process:
- Collection involves surveys, experiments, or observations.
- Organization refers to sorting data into categories or tables.
- Analysis includes calculations (mean, median, standard deviation).
- Interpretation helps make sense of the data in context.
- Presentation uses charts, graphs, and tables for clarity.
b. A statistic is a single measure, reported as a number, used to summarize a sample data set.
✅ True
A statistic refers to a numerical summary of a sample, not the whole population. Examples include the sample mean (x̄), sample proportion (p̂), or sample standard deviation (s). Since it’s based on a subset of the population, it’s used to estimate population parameters.
c. Descriptive statistics refers to generalizing from a sample to a population, estimating unknown parameters, drawing conclusions, and making decisions.
❌ False
This describes inferential statistics, not descriptive.
Descriptive statistics simply summarize or describe features of a data set, such as averages, frequencies, or standard deviations. There is no generalization or prediction. The processes described in this statement (generalization, estimation, decision-making) are hallmarks of inferential statistics.
d. One of the advantages of censuses is that they provide up-to-date data.
❌ False
While a census aims to collect data from every member of a population, it is often time-consuming and costly, making it less frequent. Therefore, the data may be outdated by the time it’s published. For instance, national censuses are typically conducted every 10 years in many countries.
e. Inferential statistics refers to the collection, organization, presentation, and summary of data, either by using charts and graphs or through numerical summaries.
❌ False
This statement actually describes descriptive statistics, not inferential.
Inferential statistics uses data from a sample to make inferences or predictions about a population. It includes tools like hypothesis testing, confidence intervals, and regression analysis—not just data presentation.
Summary of Correct Answers:
a. True
b. True
c. False
d. False
e. False