Statistics and Probability Final Exam

What is the primary purpose of statistical analysis in research?

• To make random guesses about data

• To organize and interpret data for decision-making

• To manipulate data for biased conclusions

• To avoid using numbers in problem-solving

If a dataset has a mean of 50 and a median of 30, what can be inferred about its distribution?

• The data is symmetrically distributed

• The data is skewed to the right

• The data is skewed to the left

• The data has no outliers

A teacher wants to know the average test scores of students in two different sections. What statistical measure should she use?

• Mode

• Mean

• Range

• Quartile

Given the data set {12, 15, 20, 25, 25, 30, 35}, which measure is most affected by an outlier of 100?

• Median

• Mode

• Mean

• Range

A researcher claims that a new teaching method improves students' performance. Which statistical tool is best to validate this claim?

• Descriptive statistics

• Inferential statistics

• Frequency distribution

• Bar graph

If you were asked to conduct a study on students' sleep patterns and academic performance, which statistical method would you use and why?

• Descriptive statistics to summarize sleep hours

• Correlation analysis to find relationships between sleep and grades

• Experimental study to manipulate students' sleep schedules

• Mode calculation to find the most common sleep hours

A survey found that students who use planners tend to submit assignments on time. What type of relationship does this indicate?

• Causal

• Correlational

• Random

• No relationship

Which of the following best describes the role of the median in a skewed distribution?

• It always equals the mean

• It is pulled toward the outliers

• It provides a more reliable central tendency than the mean

• It is used to measure dispersion

If a student scores at the 90th percentile on a standardized test, what does this indicate?

• The student scored 90 out of 100

• The student scored higher than 90% of test-takers

• The student answered 90% of the questions correctly

• The student received a grade of 90%

You are asked to present a statistical report on students' preferred learning styles. What would be the best method of data collection?

• Interviewing only top-performing students

• Randomly surveying students from different grade levels

• Collecting opinions from teachers

• Using past exam scores to determine preferences