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B. Determine the coefficient of skewness using Pearsons method (Round your answer to 3 decima places )c Determine the coefficient of skewness using the software met...

Question

B. Determine the coefficient of skewness using Pearsons method (Round your answer to 3 decima places )c Determine the coefficient of skewness using the software method (Round your answer to 3 decimal places_coelicient of skewness

b. Determine the coefficient of skewness using Pearsons method (Round your answer to 3 decima places ) c Determine the coefficient of skewness using the software method (Round your answer to 3 decimal places_ coelicient of skewness



Answers

A measure to determine the skewness of a distribution is called the Pearson coefficient (PC) of skewness. The formula is $$\mathrm{PC}=\frac{3(\bar{X}-\mathrm{MD})}{s}$$ The values of the coefficient usually range from $-3$ to $+3 .$ When the distribution is symmetric, the coefficient is zero; when the distribution is positively skewed, it is positive; and when the distribution is negatively skewed, it is negative. Using the formula, find the coefficient of skewness for each distribution, and describe the shape of the distribution. a. Mean = 10, median = 8, standard deviation = 3. b. Mean = 42, median = 45, standard deviation = 4. c. Mean = 18.6, median = 18.6, standard deviation = 1.5. d. Mean = 98, median = 97.6, standard deviation = 4.

This is problem # 43, we are given a formula for a distribution characteristic called skinnies formula is as follows, three times the meme minus the median, divided by our standard distribution, standard deviation. So, for part A We are given a mean of 50, a median of 40 and a standard deviation of 10. This gives us three times 50 -40, which is 10, divided by 10, Giving us units of three. So we can say that this distribution is skewed right. For part B we have a means of 100 A median of 100, so that will make the mean minus median equal to zero and a standard deviation of 15 Giving US zero. So this is a symmetric distribution. Finally, for part C, we have Three times are mean which is 400 minus our meeting, which is 500, giving us negative 100 Divided by our standard deviation, which is 120. So this will be negative 100 over 40 or could be -2.5. So this is a skewed left distribution.

So in this question, were given the formula for Pearson's index off skill nous, which is given here. And we're told that most distributions have skill nous between minus three and three. We're also told that when peace more than zero, the data is skewed right when peace less than zero skewed left and when peace equals to zero, the data is symmetric. Now we're asked to calculate the coefficient of skill nous for each off. The distributions given so first were given the mean as 17 and the standard deviation. 2.3 medium 19. So we take three times 17, minus 19 over 2.3 for part A 17 minus 19. It's minus two times 3/2 0.3 week Get an index off minus 2.60 87 for party. Now it's less than zero. So it's cute. Yeah, So we have our answer to part Kate. How in part pain. We are given a mean off 32. So we have three. 30 to minus the median which is 25 and the sample standard deviation is 5.1. So we have 30 to minus 25 times three over 5.1, which gives us whore 0.1176 So this is more than zero. The data is skewed. Right? So this is part P. Let's continue with part scene. We have the means off. 9.2, we have a median off. Also 9.2. Standard deviation off 1.8. This is going to give us zero. So this is a symmetric distribution. Hardeen. We have three times the mean, which is 40 to minus the median. Just 40 divided by six. So we have 40 to minus 40 times 3/6, which gives us one. And so, since our persons coefficient is one data, it's skewed right. And this is our uncertain part, Teen. And so we have our answers from Part A, B, C and D.

Okay, in this question, we have been given frequency tables and we have to draw their history. Grams, the first one is regarding the incomes, right. We have to develop a history, Graham for the annual income data that is given to us. So if you look at the system Graham, I have drawn on Instagram over here. We see that this is skewed to the right. And does this make sense? It actually does. Why? Because the number off rich people will decrease, right? Not everybody is going to be rich. We will see that a lot of people belong toe middle class families. So their incomes are relatively on the lower side. And the graphs should decline as we go upwards. Which means that the number off rich people actually keep on declining. So, yes, this is skewed to the right, and it makes sense. So over here, I can say that this is skewed to the right. Okay? And it does make sense. Now moving on the part B. What part do you have to say now? We have to develop a history, Graham for exam score data. So this is the history, Graham for that Over here too. We can see that This is we can say skewed to the right. Okay for this one also, we can see that it is cute. It is skewed to the right. All right. And what is the last one? The last one says we have to develop a instagram for the data that is given an exercise 11. What does the skin is? Show? This is the instagram that we have. We're here. If I change the number of classes, let's say if I just make this three and if I edit this instagram, I can see that this is sort off symmetrical. Okay, But if I change the number of classes, if I make this instagram more finer I can see that this is actually secured to the left. So this I can say that is skewed to the left. This is also skewed to the left. You know, this actually depends on the number of classes, right? Because if you increase the classes, the grab the instagram will become more finer. So the first one is to the right. So again, one is also skewed to the right and this one is skewed to the left. This is how we go about doing this question

Okay, so this is going to be the uh bottom and upper end of the confidence in the role or it's not really confidence interval X is given by the average plus the Z score times the sigma. So, were you given that knew the average is? So wait all up. It is 10 mm hmm. And the standard deviation mm sigma is three. We look up in table to to find out what the determine to interpret portals of data. So quartile is gonna be 25% of the data, first quartile and there's the middle chortled or the median at 50% And the third one that 75%. So if we find the one for 25%, the Z score of 25%,, We find that Z. It's going to be equal to negative 0.67 And then at 50% it's going to be zero And that 75%, predictably going to be 67% or .67. So our first quartile is going to be 10 plus -067 times three. Yeah. Uh Taking a calculator here. This comes out to be 7.99 almost eight. And then the second one 10 plus zero is just gonna be 10 and x three we have 10 plus 067 times three. And that is going to get us up to 12.01. Mhm. Alright obtain and interpret the seventh death style. So that would be 70% of the curve. Maybe I'll just draw this out for interpretation. Uh 50% is right here. So an extra 20 would probably be this. So 70% of the curve would be this leaving out this part. Yeah and that gets us a Z score of yeah 0.52. So ex at 0.7 the 70th percentile you have 10 plus zero 0.52 times three And this is equal to 11.56. And next find the value that 35% of all possible values of the variable exceed. So now we're looking at And that would mean that we were looking at 35%. So 35% is right here. We're looking at all the values to the right, so that would be 65% of the graph Because we have one over here and 35% here, which means that this segment here is 65. Um the Z score of 65 is 0.39. So our x at 0.35 or 65. Really We could write this as is 1 -0.35. It's going to be 10 times 039 Time Street, Which is equal to 11.17. Yeah, So 35% of all the observations Are going to be larger than 11.17. And then we can find the Z scores For the 5%. So it's gonna be at the tail ends right here and right here. Oh. Mhm. And so for lower tail, it's going to be X. Is equal to New again, still 10 plus. Actually, we're starting at the lower tail, so minus. And we see at .05% the Z score is 2.575. Yeah, So yeah, we're still adding, but this time we're multiplying by a negative, which is gonna get a negative number because our standard deviation isn't negative, And this gets us 2, 2, 75. And as for the upper, so maybe we could call this low and up. So we have 10 plus 2, +575 times three. And that gets us 17 7- five. So 99% of all of our observations are going to be between these two numbers. And that wraps up


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