If the difference of Mode and Median of a data is 24, then the differe...
We have,
Mode=3Median−2Mean
⇒Mode−Median=2(Median−Mean)
⇒24=2(Median−Mean)⇒Median−Mode=12
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If the difference of Mode and Median of a data is 24, then the differe...
The difference between the mode and median of a data set can provide insight into the distribution of the data. In this case, we are given that the difference between the mode and median is 24.
Finding the Mode:
- The mode is the value that appears most frequently in the data set.
- To find the mode, we need to identify the value(s) that occur with the highest frequency.
- Let's assume that the mode is represented by 'M'.
Finding the Median:
- The median is the middle value in a sorted data set.
- To find the median, we need to arrange the data in ascending order and locate the middle value.
- Let's assume that the median is represented by 'D'.
Calculating the Mean:
- The mean is the average of all the values in the data set.
- To find the mean, we need to sum up all the values and divide by the total number of values.
- Let's assume that the mean is represented by 'N'.
Given information: Mode - Median = 24
Using the given information, we can form the following equation:
M - D = 24
To determine the relationship between the median and mean, we need additional information. However, we can make an assumption based on the typical characteristics of data distributions.
Assumption: In a symmetric distribution, the mean, median, and mode are approximately equal.
If we assume that the mean, median, and mode are approximately equal, we can substitute 'M' for 'D' in the equation:
M - M = 24
0 = 24
This assumption leads to an inconsistency in the equation, indicating that the assumption is incorrect. Therefore, we need to reconsider our assumption.
Alternative Approach:
Instead of assuming that the mean, median, and mode are equal, let's consider another scenario where the mode is greater than the median.
Assumption: Mode > Median
In this case, we can rewrite the equation as follows:
M - D = 24
Since the mode is greater than the median, the difference between the mode and median will be positive. Therefore, we can rewrite the equation as:
(M - D) > 0
24 > 0
Now, we can see that the difference between the mode and median is positive. However, we still don't have enough information to determine the relationship between the median and mean.
Conclusion:
Based on the given information, we cannot determine the exact difference between the median and mean. Therefore, the correct answer cannot be determined from the options provided.