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Explain the difference between descriptive and inferential statistics.
Descriptive statistics describe data, while inferential statistics interpret data to make broader conclusions.
What does a positive correlation indicate?
As one variable increases, the other variable also increases.
What does a negative correlation indicate?
As one variable increases, the other variable decreases.
Explain the importance of understanding correlation vs. causation.
Correlation does not equal causation. Just because two variables are related does not mean one causes the other. Experiments are needed to prove causation.
Describe a normal distribution.
A bell-shaped and symmetrical distribution where most data clusters around the mean.
Describe a positively skewed distribution.
A distribution with a tail extending to the right, where the mean is greater than the median.
Describe a negatively skewed distribution.
A distribution with a tail extending to the left, where the median is greater than the mean.
What does a low standard deviation indicate?
Data points are clustered close to the mean.
What does a high standard deviation indicate?
Data points are more spread out from the mean.
What is the 68% rule in a normal distribution?
68% of the data falls within one standard deviation of the mean.
What is the 95% rule in a normal distribution?
95% of the data falls within two standard deviations of the mean.
How is understanding correlation used in everyday life?
Helps to interpret relationships between events, but avoid assuming causation without further evidence.
How is the concept of standard deviation applied in quality control?
Used to measure the consistency of a manufacturing process; lower SD indicates higher consistency.
How are measures of central tendency used in grading?
Teachers use mean, median, and mode to understand the typical performance of students on exams.
How is statistical significance applied in medical research?
Used to determine if the results of a clinical trial are likely due to the treatment or due to chance.
Compare the mean and the median.
Mean is the average, sensitive to outliers. Median is the middle value, resistant to outliers.
Compare standard deviation and range.
Standard deviation measures the average spread around the mean; range measures the difference between the highest and lowest values.
Compare positive and negative correlation.
Positive correlation: variables increase together. Negative correlation: as one variable increases, the other decreases.