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If the mean and the mode of a distribution are 20 and 14 respectively then the median of the distribution is?
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If the mean and the mode of a distribution are 20 and 14 respectively ...
Understanding Mean, Median, and Mode
The mean, median, and mode are the three measures of central tendency used in statistics to summarize data. In this case, we are given the mean (20) and the mode (14) of a distribution. To find the median, we can use the relationship among these three measures.
Relationship Among Mean, Median, and Mode
In a normal distribution, the mean, median, and mode are equal. However, in skewed distributions, the following relationship can be utilized:
- Mean - Mode = 3(Median - Mode)
Given:
- Mean (M) = 20
- Mode (Mo) = 14
We can rearrange the formula to solve for the median (Md):
Calculation Steps
1. Substitute the known values into the relationship:
20 - 14 = 3(Md - 14)
2. Simplify the equation:
6 = 3(Md - 14)
3. Divide both sides by 3:
2 = Md - 14
4. Solve for the median:
Md = 2 + 14
Md = 16
Conclusion
Thus, the median of the distribution is 16. This indicates that the data is positively skewed since the mean is greater than the median and mode. Understanding these relationships helps in interpreting data distributions effectively.
The mean, median, and mode are the three measures of central tendency used in statistics to summarize data. In this case, we are given the mean (20) and the mode (14) of a distribution. To find the median, we can use the relationship among these three measures.
Relationship Among Mean, Median, and Mode
In a normal distribution, the mean, median, and mode are equal. However, in skewed distributions, the following relationship can be utilized:
- Mean - Mode = 3(Median - Mode)
Given:
- Mean (M) = 20
- Mode (Mo) = 14
We can rearrange the formula to solve for the median (Md):
Calculation Steps
1. Substitute the known values into the relationship:
20 - 14 = 3(Md - 14)
2. Simplify the equation:
6 = 3(Md - 14)
3. Divide both sides by 3:
2 = Md - 14
4. Solve for the median:
Md = 2 + 14
Md = 16
Conclusion
Thus, the median of the distribution is 16. This indicates that the data is positively skewed since the mean is greater than the median and mode. Understanding these relationships helps in interpreting data distributions effectively.
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If the mean and the mode of a distribution are 20 and 14 respectively then the median of the distribution is?
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If the mean and the mode of a distribution are 20 and 14 respectively then the median of the distribution is? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about If the mean and the mode of a distribution are 20 and 14 respectively then the median of the distribution is? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the mean and the mode of a distribution are 20 and 14 respectively then the median of the distribution is?.
If the mean and the mode of a distribution are 20 and 14 respectively then the median of the distribution is? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about If the mean and the mode of a distribution are 20 and 14 respectively then the median of the distribution is? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the mean and the mode of a distribution are 20 and 14 respectively then the median of the distribution is?.
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