What measures central tendency and spread in a binomial distribution?

What measures central tendency and spread in a binomial distribution?

• A. The median and range
• B. The mean and variance
• C. The mode and interquartile range
• D. The mean and standard deviation

Answer: (B)

In the context of a binomial distribution, the mean and variance are the key measures of central tendency and spread, respectively. The mean of a binomial distribution, calculated as \( n \times p \) (where \( n \) is the number of trials and \( p \) is the probability of success), provides a measure of the central value around which the outcomes are expected to cluster. This value indicates the average number of successes in the given number of trials. The variance, determined using the formula \( n \times p \times (1 - p) \), quantifies the degree to which the outcomes can vary. A higher variance signifies a larger spread around the mean, while a lower variance indicates that the outcomes are more closely clustered around the mean. These two calculations together give a comprehensive view of the behavior of outcomes in a binomial distribution: the mean indicates where the center lies, and the variance describes how wide the distribution is around that center. Therefore, they effectively represent the central tendency and spread of a binomial distribution.

In the context of a binomial distribution, the mean and variance are the key measures of central tendency and spread, respectively.

The mean of a binomial distribution, calculated as ( n \times p ) (where ( n ) is the number of trials and ( p ) is the probability of success), provides a measure of the central value around which the outcomes are expected to cluster. This value indicates the average number of successes in the given number of trials.

The variance, determined using the formula ( n \times p \times (1 - p) ), quantifies the degree to which the outcomes can vary. A higher variance signifies a larger spread around the mean, while a lower variance indicates that the outcomes are more closely clustered around the mean.

These two calculations together give a comprehensive view of the behavior of outcomes in a binomial distribution: the mean indicates where the center lies, and the variance describes how wide the distribution is around that center. Therefore, they effectively represent the central tendency and spread of a binomial distribution.