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Descriptive Statistics
Measures of Central Tendency
Mean: The average of a set of numbers, calculated by dividing the sum of the values by the number of values. It is sensitive to outliers.
Median: The middle value in a dataset when the values are arranged in ascending or descending order. It is less affected by outliers and skewed data.
Mode: The value that appears most frequently in a dataset. A dataset can have more than one mode or no mode at all.
Measures of Dispersion
Range: The difference between the highest and lowest values in a dataset. It provides a quick sense of the spread of the data.
Variance: A measure of how much the values in a dataset differ from the mean. It is calculated as the average of the squared differences from the mean.
Standard Deviation: The square root of the variance, indicating how spread out the values are from the mean. A low standard deviation means the values are close to the mean, while a high standard deviation indicates the values are spread out.
Visualizing Data
Histograms: Used to represent the frequency distribution of a dataset. It shows how many data points fall into each range of values.
Box Plots: Show the distribution of data based on a five-number summary: minimum, first quartile, median, third quartile, and maximum. It helps in identifying outliers and the spread of the data.
Quiz
1. What does descriptive statistics aim to do?
- a) Infer conclusions about a population
- b) Summarize and describe the main features of a dataset
- c) Visualize data
- d) Test hypotheses
2. True or False: The median is the average of a dataset.
- a) True
- b) False
3. What does the range of a dataset represent?
- a) The most frequently occurring value
- b) The difference between the highest and lowest values
- c) The average value
- d) The middle value
4. Which measure of dispersion indicates the average distance of each data point from the mean?
- a) Range
- b) Variance
- c) Standard deviation
- d) Interquartile range
5. What type of graph is used to display the frequency distribution of a dataset?
- a) Bar chart
- b) Line graph
- c) Histogram
- d) Pie chart
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