Statistics refers to the practice or science of collecting, organizing, analyzing, interpreting, and presenting numerical data. Descriptive statistics is a branch of statistics that involves organizing, summarizing, and presenting data in a meaningful way. It helps us understand the main features of a set of data without making any conclusions beyond what is observed.
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Mean (Average):
- Definition: The mean is the sum of all values in a data set divided by the number of values.
- Example: Suppose we have test scores of 5 students: 80, 85, 90, 75, 95. The mean is (80 + 85 + 90 + 75 + 95) / 5 = 85.
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Median:
- Definition: The median is the middle value in a sorted list of numbers. If there is an even number of values, it's the average of the two middle numbers.
- Example: For the set of test scores (75, 80, 85, 90, 95), the median is 85. If we add another score, say 92, the median becomes (85 + 90) / 2 = 87.5.
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Mode:
- Definition: The mode is the value that appears most frequently in a data set.
- Example: In the set of test scores (75, 80, 85, 90, 95), there is no mode because each score appears only once. If we add another 85, then 85 becomes the mode.
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Range:
- Definition: The range is the difference between the maximum and minimum values in a data set.
- Example: For the test scores (75, 80, 85, 90, 95), the range is 95 - 75 = 20.
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Standard Deviation:
- Definition: Standard deviation measures the amount of variation or dispersion in a set of values.
- Example: If we have two sets of test scores, one with scores (80, 85, 90, 95, 100) and another with scores (70, 75, 80, 85, 90), both sets have the same mean (90), but the second
has a smaller standard deviation, indicating less variation.