Anonymous
Jul 1
The median and standard deviation of 50 observation are 25 and 6 respectively.find the second person measure of skewness if the sum of the observations is 900.comment on your answer?
1 view
1 view
2 answers
Sort By
ChatGPT
Jul 1
To find the second Pearson measure of skewness, we can use the formula:
Skewness = 3 * (Mean - Median) / Standard Deviation
Given that the median is 25 and the standard deviation is 6, we need to find the mean. We know that the sum of the observations is 900 and there are 50 observations, so the mean can be calculated as:
Mean = Sum of observations / Number of observations
Mean = 900 / 50
Mean = 18
Now we can plug the values into the formula:
Skewness = 3 * (18 - 25) / 6
Skewness = 3 * (-7) / 6
Skewness = -21 / 6
Skewness = -3.5
Therefore, the second Pearson measure of skewness is -3.5.
A skewness value of -3.5 indicates that the distribution is highly negatively skewed, meaning that the tail of the distribution is longer on the left side. This suggests that there are more observations on the lower end of the distribution compared to the higher end.
Skewness = 3 * (Mean - Median) / Standard Deviation
Given that the median is 25 and the standard deviation is 6, we need to find the mean. We know that the sum of the observations is 900 and there are 50 observations, so the mean can be calculated as:
Mean = Sum of observations / Number of observations
Mean = 900 / 50
Mean = 18
Now we can plug the values into the formula:
Skewness = 3 * (18 - 25) / 6
Skewness = 3 * (-7) / 6
Skewness = -21 / 6
Skewness = -3.5
Therefore, the second Pearson measure of skewness is -3.5.
A skewness value of -3.5 indicates that the distribution is highly negatively skewed, meaning that the tail of the distribution is longer on the left side. This suggests that there are more observations on the lower end of the distribution compared to the higher end.
0
Google Gemini AI
Jul 1
Step 1: Calculate the mean
The sum of the observations is 900, so the mean (average) is:
Mean = Sum of observations / Number of observations
Mean = 900 / 50 = 18
Step 2: Calculate the third central moment
The third central moment (skewness) is a measure of how asymmetric a distribution is. It is calculated as:
Skewness = (1 / n) - Σ[(x - mean)^3]
Where:
- n is the number of observations
- x is each observation
- mean is the mean of the observations
We do not have the individual observations, so we cannot calculate the skewness directly. However, we can use the median and standard deviation to estimate the skewness.
Step 3: Estimate the skewness
There are several methods for estimating skewness from the median and standard deviation. One common method is:
Skewness ≈ 3 - (Median - Mean) / Standard Deviation
Substituting the given values:
Skewness ≈ 3 - (25 - 18) / 6
Skewness ≈ 3 - 7 / 6
Skewness ≈ 3.5
Conclusion
Based on this estimation, the distribution of the observations is positively skewed. This means that there are more observations above the median than below it, and the distribution has a tail extending to the right. The estimated skewness of 3.5 is considered moderate to high, indicating a substantial departure from symmetry.
The sum of the observations is 900, so the mean (average) is:
Mean = Sum of observations / Number of observations
Mean = 900 / 50 = 18
Step 2: Calculate the third central moment
The third central moment (skewness) is a measure of how asymmetric a distribution is. It is calculated as:
Skewness = (1 / n) - Σ[(x - mean)^3]
Where:
- n is the number of observations
- x is each observation
- mean is the mean of the observations
We do not have the individual observations, so we cannot calculate the skewness directly. However, we can use the median and standard deviation to estimate the skewness.
Step 3: Estimate the skewness
There are several methods for estimating skewness from the median and standard deviation. One common method is:
Skewness ≈ 3 - (Median - Mean) / Standard Deviation
Substituting the given values:
Skewness ≈ 3 - (25 - 18) / 6
Skewness ≈ 3 - 7 / 6
Skewness ≈ 3.5
Conclusion
Based on this estimation, the distribution of the observations is positively skewed. This means that there are more observations above the median than below it, and the distribution has a tail extending to the right. The estimated skewness of 3.5 is considered moderate to high, indicating a substantial departure from symmetry.
0
