Answer :
The absolute difference between the mean and mode is (b.) the mean minus the mode.
Mean (μ): The average value of the distribution, calculated as the sum of all values weighted by their probabilities.
Mode: The value that appears most frequently in the distribution.
To find the absolute difference between the mean and the mode, we use the following formula:
Absolute difference = |Mean - Mode|
This calculation determines the magnitude of difference without regard to direction (i.e., whether the mean is greater than or less than the mode).
Calculation Example:
If the mean of a distribution is 10 and the mode is 7, the absolute difference is calculated as: |10 - 7| = 3
Final answer:
The absolute difference between the mean and mode of a probability function is calculated by finding the non-negative value of the difference between these two measures. Since the options provided do not explicitly mention taking the absolute value, and c) and d) include the median which is incorrect, none of the multiple-choice options provided are technically correct.
Explanation:
The question pertains to the calculation of the absolute difference between the mean and mode of a probability function. It is important to understand that mean denotes the average of a set of values, mode signifies the most frequently occurring value, and median is the middle value when the numbers are arranged in order.
For a symmetrical distribution, the mean, median, and mode coincide, meaning they are the same. However, in a skewed distribution, these measures of central tendency can differ. Specifically, if the distribution is skewed to the left, the mean will be less than the median, which will, in turn, be less than the mode. Conversely, if the distribution is skewed to the right, the mode will be less than the median, which will be less than the mean.
In terms of the absolute difference between the mean and the mode, you would calculate it by finding the absolute value of the difference between these two measures to ensure a non-negative result. Therefore, the correct answer to the question is neither a) The mode minus the mean nor b) The mean minus the mode because both do not mention taking the absolute value. Options c) and d) cannot be the answer since they involve the median, not the mean. However, since the median is not involved in the calculation, choice c) The median minus the mode and d) The mode minus the median are also incorrect.
