Question

which of the following is a measure of central tendency?
a. range
b. mean
c. variance
d. standard deviation

Explanation:

• Mean: It is a measure of central tendency. It represents the average of a set of data values. For example, if we have data points \(x_1,x_2,\cdots,x_n\), the mean \(\bar{x}=\frac{\sum_{i = 1}^{n}x_i}{n}\).
• Range: It is a measure of dispersion. It is calculated as \(Range=\text{Max value}-\text{Min value}\) in a data - set.
• Variance: It is a measure of dispersion. For a sample of data \(x_1,x_2,\cdots,x_n\) with sample mean \(\bar{x}\), the sample variance \(s^2=\frac{\sum_{i = 1}^{n}(x_i - \bar{x})^2}{n - 1}\).
• Standard deviation: It is also a measure of dispersion. It is the square - root of the variance. For a sample, \(s=\sqrt{\frac{\sum_{i = 1}^{n}(x_i - \bar{x})^2}{n - 1}}\).

Answer:

B. Mean