Introduction:
In a moderately skewed distribution, the values of mean and median are given as 12 and 8 respectively. We need to find out the value of mode.

Meaning of Skewed Distribution:
A skewed distribution is a statistical term that refers to the asymmetry of a probability distribution. In a skewed distribution, the tail of the distribution is either longer or shorter than the other tail. A long tail means that there are some values that are much larger than the majority of the values in the distribution. A short tail means that there are some values that are much smaller than the majority of the values in the distribution.

Meaning of Mode:
In statistics, the mode is the value that appears most frequently in a data set. A set of data may have one mode, more than one mode, or no mode at all.

Solution:
To find the mode, we need to know the shape of the distribution. Since the distribution is moderately skewed, we can assume that it is not perfectly symmetrical. We know that the median is 8, which means that half of the values in the distribution are less than 8 and half are greater than 8. We also know that the mean is 12, which means that if we take the sum of all the values in the distribution and divide by the total number of values, we get 12.

Since the distribution is skewed, the mode may not be the same as the mean or median. However, we can use the mean and median to make an educated guess about the mode. If the distribution is skewed to the right (i.e., has a long tail on the right-hand side), the mode is likely to be less than the median and less than the mean. If the distribution is skewed to the left (i.e., has a long tail on the left-hand side), the mode is likely to be greater than the median and greater than the mean.

In our case, since the mean is greater than the median, we can assume that the distribution is skewed to the right. Therefore, the mode is likely to be less than the median and less than the mean. Based on this information, we can make an educated guess that the mode is less than 8. However, we cannot determine the exact value of the mode without more information.

Conclusion:
In summary, we know that in a moderately skewed distribution, the values of mean and median are 12 and 8 respectively. We also know that the mode is the value that appears most frequently in a data set. However, since we do not have enough information about the distribution, we cannot determine the exact value of the mode. We can only make an educated guess that the mode is less than 8.

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