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Descriptive statistics involve summarizing and organizing data so it can be easily understood. Descriptive statistics are typically broken down into two categories:

**Measures of Central Tendency**: These describe the center or typical value of a dataset. Common measures include:**Mean**: The average of all data points.**Median**: The middle value when the data is ordered from least to greatest.**Mode**: The most frequently occurring value(s) in a dataset.

**Measures of Dispersion (or Variability)**: These describe the spread of the data. Common measures include:**Range**: The difference between the maximum and minimum values.**Variance**: The average of the squared differences from the mean.**Standard Deviation**: The square root of the variance, indicating the average amount each data point differs from the mean.**Interquartile Range (IQR)**: The range within the middle 50% of the data, calculated as the difference between the 75th and 25th percentiles.

**Other Descriptive Statistics**:**Skewness**: A measure of the asymmetry of the distribution of values.**Kurtosis**: A measure of the “tailedness” of the distribution of values.**Percentiles**: Values below which a certain percentage of data points in a dataset fall.

### Example

Letâ€™s say we have a dataset of exam scores: [55, 63, 77, 85, 88, 92, 94, 97, 99, 100].

**Central Tendency**:**Mean**: (55 + 63 + 77 + 85 + 88 + 92 + 94 + 97 + 99 + 100) / 10 = 85**Median**: (88 + 92) / 2 = 90**Mode**: No mode, as all values are unique.

**Dispersion**:**Range**: 100 – 55 = 45**Variance**:- First, find the mean (85).
- Calculate each data pointâ€™s deviation from the mean, square it, and find the average of those squared deviations.
- Variance = [(55-85)Â² + (63-85)Â² + (77-85)Â² + (85-85)Â² + (88-85)Â² + (92-85)Â² + (94-85)Â² + (97-85)Â² + (99-85)Â² + (100-85)Â²] / 10
- Variance = 184.4

**Standard Deviation**: âˆš184.4 â‰ˆ 13.58**IQR**:- Q1 (25th percentile) = 77
- Q3 (75th percentile) = 97
- IQR = 97 – 77 = 20

**Other Statistics**:**Skewness**: Since the mean is less than the median, the distribution is slightly left-skewed.**Kurtosis**: Calculated as part of a more complex formula, typically requiring statistical software for exact value.

These statistics provide a comprehensive summary of the datasetâ€™s characteristics, giving a clear picture of its central tendency, spread, and overall distribution shape.