Describe the commonly used measures of central tendency. Explain any one qualitative technique used for research.
Measures of central tendency are statistical measures that describe where the center of a distribution of data points lies. They provide a single value that represents the "middle" or "typical" value of a dataset. The three commonly used measures of central tendency are:
1. Mean:
- The mean, also known as the average, is the sum of all values in a dataset divided by the number of values.
- Formula: \(\bar{x} = \frac{\sum_{i=1}^{n} x_i}{n}\), where \(\bar{x}\) is the mean, \(x_i\) are individual data points, and \(n\) is the number of data points.
- Example: If you have test scores of 80, 85, 90, and 95, the mean score is \(\frac{80 + 85 + 90 + 95}{4} = 87.5\).
2. Median:
- The median is the middle value in a dataset when the values are arranged in ascending or descending order.
- If there is an odd number of observations, the median is the middle value. If there is an even number, it is the average of the two middle values.
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