The sum of fifteen observation,whose mode is 8,was found to be 150 with coefficient of variation of 20% a calculate the pearsonian coeffiient of skeweness and give appropriate conculation bare smallervalues more or less frequent than bigger values for this disterbution? c if a constant 4 was added on each observation ,what will be the new pearsonian coefficient of skewness? shaw your steps. what do you conclude from this?
Answers
Explanation:
answer is in attachment
Answer:
Determine the mean and standard deviation of the distribution before calculating the Pearson coefficient of skewness. If there are 150 observations, we may calculate that 15 is 10.
Explanation:
Because we also have the coefficient of variation ( = 0.2), we can use it to calculate the standard deviation:
A standard deviation is the coefficient of variation multiplied by the mean, 10.
Here's the formula for determining the skewness as measured by the Pearsons:
Skewness, as measured by the Pearsonian coefficient, = 3 * (mean - mode) / SD
With the values we are familiar with, we get:
For a skewness value of 3 according to the Pearsonian formula, you would need to multiply (3 + 10 - 8)/(2 + 2).
With a Pearsonian skewness value of 3, the distribution is very right-skewed, having a very long tail to the right of the mean.
We may infer that smaller values are less common than larger ones in this distribution since their Pearsonian coefficient of skewness is larger than the other way around. The right-hand tail of the distribution is on the right side of the mode because the coefficient of skewness is positive. Hence, there are more reports of high numbers than low ones.
The new observations total is (150 + 15 * 4 = 210), if we add a constant 4 to each one. To illustrate, if we were to add a constant to each observation, the new mean would be 210/15 = 14, and the new SD would still be 2.
The new coefficient may be computed using the Pearsonian coefficient of skewness formula:
We may calculate the skewness using the Pearsonian formula: = 3 * (mean - mode) / SD = 3 * (14 - 8) / 2 = 9.
The increased skewness of the new Pearsonian coefficient is denoted by the number 9. Hence, the distribution is now much more skewed to the right, with a larger tail to the right of the median.
Overall, the Pearsonian coefficient of skewness for the initial distribution was 3, suggesting extreme skewness towards bigger values. The skewness was unaffected by adding a constant of 4 to each observation, but the coefficient rose to 9 (showing an even more skewed distribution).
To learn more about standard deviation, click on the link below.
https://brainly.com/question/475676
To learn more about the Pearson coefficient, click on the link below.
https://brainly.in/question/52238492
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