Question-1

Descriptive statistics and inferential statistics are two main branches of statistics used to analyze data. Descriptive statistics is concerned with summarizing and describing data, while inferential statistics is focused on making inferences about a population based on sample data.

Descriptive statistics is used to describe the characteristics of a data set, including measures of central tendency such as mean, median, and mode, measures of dispersion such as range, variance, and standard deviation, and visual representations such as histograms, scatter plots, and box plots. For example, if we want to describe the average income of a group of people, we can use descriptive statistics to calculate the mean income, median income, and the range of income values.

Inferential statistics, on the other hand, uses sample data to make inferences about a population. Inferential statistics is used to estimate parameters of a population, such as mean or standard deviation, based on the data collected from a sample of the population. For example, if we want to estimate the average income of the entire population, we can collect a sample of data from the population, calculate the mean income of the sample, and use inferential statistics to estimate the mean income of the entire population.

Another example of the difference between descriptive and inferential statistics is in clinical trials. Descriptive statistics can be used to summarize the data on the participants, such as their age, gender, and medical history. Inferential statistics can then be used to make conclusions about the effectiveness of a new drug by comparing the outcomes of the group that received the drug to the outcomes of the group that received a placebo.

In summary, descriptive statistics is used to summarize and describe data, while inferential statistics is used to make inferences about a population based on sample data. Both types of statistics are essential in analyzing and interpreting data.