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In Uni-model distribution, if mode is less than mean, then the distribution will be_________.
- a)Symmetrical
- b)Normal
- c)Positively skewed
- d)Negatively skewed
Correct answer is option 'D'. Can you explain this answer?
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In Uni-model distribution, if mode is less than mean, then the distrib...
Explanation:
Uni-model Distribution:
A unimodal distribution is a type of probability distribution that has only one peak or mode.
Mode, Mean, and Skewness:
- The mode is the value that appears most frequently in a data set.
- The mean is the average of all the values in a data set.
- Skewness is a measure of the asymmetry of a distribution.
Relationship between Mode, Mean, and Skewness:
- If the mode is less than the mean, it means that the data is skewed to the left or negatively skewed.
- In a negatively skewed distribution, the tail of the distribution is longer on the left side of the peak, and the mean is less than the mode.
Conclusion:
Therefore, if the mode is less than the mean in a unimodal distribution, the distribution will be negatively skewed. This indicates that the data is concentrated on the right side of the peak, with a longer tail on the left side.
Uni-model Distribution:
A unimodal distribution is a type of probability distribution that has only one peak or mode.
Mode, Mean, and Skewness:
- The mode is the value that appears most frequently in a data set.
- The mean is the average of all the values in a data set.
- Skewness is a measure of the asymmetry of a distribution.
Relationship between Mode, Mean, and Skewness:
- If the mode is less than the mean, it means that the data is skewed to the left or negatively skewed.
- In a negatively skewed distribution, the tail of the distribution is longer on the left side of the peak, and the mean is less than the mode.
Conclusion:
Therefore, if the mode is less than the mean in a unimodal distribution, the distribution will be negatively skewed. This indicates that the data is concentrated on the right side of the peak, with a longer tail on the left side.
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Community Answer
In Uni-model distribution, if mode is less than mean, then the distrib...
A unimodal distribution refers to a distribution that has a single peak or mode. It means that there is one value in the dataset that occurs more frequently than any other value.
When the mode is less than the mean, it indicates that the majority of the data points are located towards the higher values, while the tail extends towards the lower values. This pattern is commonly observed in negatively skewed distributions, also known as left-skewed distributions.
In a negatively skewed distribution, the tail extends towards the left side, while the bulk of the data is concentrated towards the right side. The mode represents the most frequently occurring value, and when it is lower than the mean, it suggests that the distribution is pulled towards the higher values.
To visualize this, imagine a dataset representing the test scores of a group of students. If the distribution is negatively skewed and the mode is less than the mean, it implies that there are a few students who scored exceptionally high, which extends the tail towards the left. However, the majority of the students have lower scores, resulting in the mode being lower than the mean.
Therefore, based on the given information, in a unimodal distribution where the mode is less than the mean, the distribution will most likely be negatively skewed. The tail of the distribution is longer on the left side, indicating a concentration of values towards the right side.
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In Uni-model distribution, if mode is less than mean, then the distribution will be_________.a)Symmetricalb)Normalc)Positively skewedd)Negatively skewedCorrect answer is option 'D'. Can you explain this answer?
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