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The distribution in which mean = 60 and mode = 50, will be ________
- a)Symmetrical
- b)Positive skewed
- c)Negative skewed
- d)None of these
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
The distribution in which mean = 60 and mode = 50, will be ________a)S...
Explanation:
To understand why the given distribution is positively skewed, let's first discuss what skewness is.
Skewness:
Skewness is a measure of the asymmetry of a probability distribution. It tells us whether the data is concentrated more on one side of the distribution or the other. Skewness can be positive, negative, or zero.
Positive Skewness:
A distribution is positively skewed when the tail on the right side of the distribution is longer or fatter than the left side. In other words, the mean is greater than the median and mode.
Mean, Median, and Mode:
The mean, median, and mode are measures of central tendency.
- Mean: The mean is the average of all the values in the distribution. It is calculated by summing up all the values and dividing by the total number of values.
- Median: The median is the middle value of the distribution when the data is arranged in ascending or descending order. It divides the data into two equal halves.
- Mode: The mode is the value that appears most frequently in the distribution.
Given Information:
- Mean = 60
- Mode = 50
Analysis:
In a positively skewed distribution, the mean is greater than the median and mode. Since the given mean is 60 and the mode is 50, we can conclude that the distribution is positively skewed.
Example:
Let's consider an example to understand this better. Assume we have the following dataset: 50, 50, 50, 60, 70, 80.
- Mean: (50 + 50 + 50 + 60 + 70 + 80) / 6 = 360 / 6 = 60
- Median: 55 (middle value)
- Mode: 50 (most frequently occurring value)
In this example, the mean is 60, which is greater than the median (55) and mode (50). Therefore, the distribution is positively skewed.
Conclusion:
Based on the given information, the distribution in which the mean is 60 and the mode is 50 is positively skewed.
To understand why the given distribution is positively skewed, let's first discuss what skewness is.
Skewness:
Skewness is a measure of the asymmetry of a probability distribution. It tells us whether the data is concentrated more on one side of the distribution or the other. Skewness can be positive, negative, or zero.
Positive Skewness:
A distribution is positively skewed when the tail on the right side of the distribution is longer or fatter than the left side. In other words, the mean is greater than the median and mode.
Mean, Median, and Mode:
The mean, median, and mode are measures of central tendency.
- Mean: The mean is the average of all the values in the distribution. It is calculated by summing up all the values and dividing by the total number of values.
- Median: The median is the middle value of the distribution when the data is arranged in ascending or descending order. It divides the data into two equal halves.
- Mode: The mode is the value that appears most frequently in the distribution.
Given Information:
- Mean = 60
- Mode = 50
Analysis:
In a positively skewed distribution, the mean is greater than the median and mode. Since the given mean is 60 and the mode is 50, we can conclude that the distribution is positively skewed.
Example:
Let's consider an example to understand this better. Assume we have the following dataset: 50, 50, 50, 60, 70, 80.
- Mean: (50 + 50 + 50 + 60 + 70 + 80) / 6 = 360 / 6 = 60
- Median: 55 (middle value)
- Mode: 50 (most frequently occurring value)
In this example, the mean is 60, which is greater than the median (55) and mode (50). Therefore, the distribution is positively skewed.
Conclusion:
Based on the given information, the distribution in which the mean is 60 and the mode is 50 is positively skewed.
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Community Answer
The distribution in which mean = 60 and mode = 50, will be ________a)S...
In a distribution, the mean, mode, and median are measures of central tendency that provide insights into the location or center of the data. However, they can have different values in different types of distributions.
Given that the mean is 60 and the mode is 50, it suggests that the majority of the values are below the mean but are concentrated around the mode. This situation typically occurs in positively skewed distributions, also known as right-skewed distributions.
In a positively skewed distribution, the tail extends towards the right side, while the bulk of the data is concentrated towards the left side. The mode represents the most frequently occurring value, and when it is lower than the mean, it indicates a concentration of values on the left side.
To illustrate this, imagine a dataset representing the ages of a group of people. If the distribution is positively skewed and the mean is higher than the mode, it implies that there are a few individuals with very high ages, which extends the tail towards the right. However, the majority of the individuals have lower ages, resulting in the mode being lower than the mean.
Therefore, based on the given information, the distribution in which the mean is 60 and the mode is 50 will most likely be positively skewed. The tail of the distribution is longer on the right side, indicating a concentration of values towards the left side.
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The distribution in which mean = 60 and mode = 50, will be ________a)Symmetricalb)Positive skewedc)Negative skewedd)None of theseCorrect answer is option 'B'. Can you explain this answer?
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