If in an asymmetrical distribution, the median is 29 and the mean is 3...
Calculation:
The formula 3 median = mode + 2 mean is an empirical relationship that may hold true for approximately symmetric distributions.
Substituting the value in the formula we get,
3 ∗ (39) = Mode + 2 ∗ (37)
Mode = 13
Mode is the value that occurs most frequently.
Median is the middle value when the dataset is arranged in order.
Mean is the sum of all values divided by the number of values.
If in an asymmetrical distribution, the median is 29 and the mean is 3...
Given:
- Asymmetrical distribution
- Median = 29
- Mean = 37
To find:
Value of the mode
Explanation:
In an asymmetrical distribution, the mode is the value that occurs most frequently. Unlike the median and mean, the mode does not necessarily have to be in the center or average of the distribution. It can be any value that occurs with the highest frequency.
Step 1: Understanding the median
The median is the middle value of the distribution when the data is arranged in ascending or descending order. In an asymmetrical distribution, the median divides the data into two halves, with an equal number of data points on each side.
Given that the median is 29, it means that there are an equal number of data points below and above 29 in the distribution.
Step 2: Understanding the mean
The mean is the average of all the data points in the distribution. In an asymmetrical distribution, the mean may not be equal to the median because the data is not symmetrically distributed around the mean.
Given that the mean is 37, it indicates that the sum of all the data points divided by the number of data points is equal to 37.
Step 3: Finding the mode
Since the distribution is asymmetrical, we cannot determine the exact value of the mode without additional information. However, we can make an inference based on the given information.
In an asymmetrical distribution, the mode is often closer to the median than the mean. This is because the mode represents the value that occurs most frequently, and in an asymmetrical distribution, the most frequent values tend to cluster around the median.
Given that the median is 29 and the mean is 37, we can infer that the mode is likely to be a value less than 29, closer to the median. Among the given options, the value 13 (option B) is the only value that satisfies this condition.
Therefore, the value of the mode in this asymmetrical distribution is 13.
Answer:
The value of the mode is 13 (option B).
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