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 observation is 900? Comment your answer?

To find the second Pearson measure of skewness, we first need to calculate the mean of the observations. Since the median is 25 and the sum of the observations is 900, the mean can be calculated as:

Mean = (Sum of observations) / (Number of observations)
Mean = 900 / 50
Mean = 18

Next, we calculate the third moment about the mean, which is the sum of the cubed deviations from the mean divided by the number of observations:

Third moment = Σ(xi - mean)^3 / n

Since we know the standard deviation is 6, we can use the formula for the third moment in terms of the standard deviation:

Third moment = Σ(xi - mean)^3 / n = (Σ(xi - mean)^3) / (n * (standard deviation)^3)

The second Pearson measure of skewness is then calculated as:

Second Pearson measure of skewness = Third moment / (standard deviation)^3

Without the actual observations, it is not possible to calculate the second Pearson measure of skewness.

The second Pearson measure of skewness is given by:

$$S=\frac{3(\mu-Me)}{s}$$

where:

- S is the skewness coefficient
- μ is the mean
- Me is the median
- s is the standard deviation

We are given that the median is 25, the standard deviation is 6, and the sum of the observations is 900. We can calculate the mean as:

$$\mu=\frac{\sum x}{n}=\frac{900}{50}=18$$

Now we can plug these values into the formula for skewness:

$$S=\frac{3(18-25}{6}=\frac{3(-7)}{6}=-3.5$$

Therefore, the second Pearson measure of skewness is -3.5. This indicates that the distribution is negatively skewed, meaning that the tail of the distribution is longer on the left side than on the right side.