If mean is less than mode, the distribution will be__________.a)Positi...
Skewness refers to the asymmetry or lack of symmetry in a distribution. It describes the extent to which the data points are skewed to the left or right of the central value.
When the mean is less than the mode, it indicates that the tail of the distribution is longer on the left side, pulling the mean towards the left. This implies that the distribution is negatively skewed, also known as left-skewed.
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 greater than the mean, it suggests that the peak of the distribution is on the right side.
To visualize this, imagine a dataset representing the incomes of a group of individuals. If the distribution is negatively skewed and the mean is less than the mode, it means that there are a few individuals with extremely low incomes, which extends the tail towards the left. The majority of the individuals have higher incomes, which creates the peak or mode on the right side.
In summary, if the mean is less than the mode, the distribution will be negatively skewed. The tail of the distribution is longer on the left side, indicating a concentration of values towards the right side.
If mean is less than mode, the distribution will be__________.a)Positi...
Introduction:
In statistics, skewness is a measure of the asymmetry of a probability distribution. It indicates the extent to which the data is concentrated to one side of the mean compared to the other side. A positively skewed distribution has a long tail on the right side, while a negatively skewed distribution has a long tail on the left side.
Mean and Mode:
The mean is the average of a set of numbers, calculated by summing all the values and dividing by the total number of values. The mode, on the other hand, is the value that appears most frequently in a dataset. It represents the peak or highest point of the distribution.
Explanation:
When the mean is less than the mode, it indicates that the data is concentrated towards the higher values and there are a few extremely low values that pull the mean down. This situation leads to a negatively skewed distribution.
Example:
Let's consider an example to understand this concept better. Suppose we have a dataset of 10 numbers: {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. The mean of this dataset is (1+2+3+4+5+6+7+8+9+10)/10 = 5.5. However, the mode of this dataset is 1, as it appears most frequently.
If we plot a histogram of this dataset, we would observe that the data is concentrated towards the higher values (5, 6, 7, 8, 9, 10) and there is a long tail towards the lower values (1, 2, 3, 4). This distribution would be classified as negatively skewed.
Conclusion:
In conclusion, when the mean is less than the mode, it indicates a concentration of data towards higher values and a long tail towards lower values. This leads to a negatively skewed distribution. Therefore, the correct answer to the given question is option 'B' - Negatively skewed.
To make sure you are not studying endlessly, EduRev has designed UPSC study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in UPSC.