True or False
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 answer and explanation is :
Here are the answers:
a. True
b. True
c. False
d. False
e. False
Explanation (300 words)
(a) True
Statistics is indeed defined as the science of collecting, organizing, analyzing, interpreting, and presenting data. It provides methods for making sense of numerical information and for making informed decisions under uncertainty. These five components are fundamental to all statistical processes, whether descriptive or inferential.
(b) True
A statistic is a numerical value that describes a characteristic of a sample. For example, the sample mean, sample standard deviation, or sample proportion are all statistics. They are used to summarize and make sense of the data collected from a subset of a population.
(c) False
This statement actually describes inferential statistics, but incorrectly labels it as descriptive statistics. Descriptive statistics involve organizing and summarizing data using tables, charts, and numerical measures like means or medians. In contrast, inferential statistics involves making predictions, inferences, or generalizations about a population based on a sample.
(d) False
While censuses aim to gather data from an entire population and can be very accurate, they are not typically up-to-date, as they are conducted infrequently due to their cost and scale. For example, the U.S. Census is conducted every 10 years. By the time data is fully collected and analyzed, some of it may already be outdated. Surveys or samples, although less comprehensive, are often more current.
(e) False
This description refers to descriptive statistics, not inferential statistics. Inferential statistics goes beyond simply describing data; it uses probability theory to make conclusions or predictions about a larger population based on sample data.
In summary, understanding the difference between descriptive and inferential statistics is crucial to applying the correct methods and drawing valid conclusions in data analysis.
