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You conduct study to find out about the range of salaries for members of the community in Hartsville The data you obtain about 183 community members organized into ...

Question

You conduct study to find out about the range of salaries for members of the community in Hartsville The data you obtain about 183 community members organized into the histogram below; Salaries of Hartsville Community Members[0-10,000 10,001-20,0000,001-30,00c0,001-40,00Ci0,001-50,00g0,001-60,0060,001-70,0000,001-80,Oo0,001-90,0020,001-100,000 Salary Estimate the median salary for Hartsville community members Enter = mmberEstimate the sample mean salary of the 183 community members; Round your a

You conduct study to find out about the range of salaries for members of the community in Hartsville The data you obtain about 183 community members organized into the histogram below; Salaries of Hartsville Community Members [ 0-10,000 10,001-20,0000,001-30,00c0,001-40,00Ci0,001-50,00g0,001-60,0060,001-70,0000,001-80,Oo0,001-90,0020,001-100,000 Salary Estimate the median salary for Hartsville community members Enter = mmber Estimate the sample mean salary of the 183 community members; Round your answer to the nearest penny; Enter number Estimate the sample standard deviation for the 183 community members: Round your answer t0 the nearest penny:



Answers

Sample annual salaries (in thousands of dollars) for employees at a company are listed. $\begin{array}{lllllll}42 & 36 & 48 & 51 & 39 & 39 & 42 \\ 36 & 48 & 33 & 39 & 42 & 45\end{array}$ (a) Find the sample mean and the sample standard deviation. (b) Each employee in the sample receives a $5 \%$ raise. Find the sample mean and the sample standard deviation for the revised data set. (c) To calculate the monthly salary, divide each original salary by $12 .$ Find the sample mean and the sample standard deviation for the revised data set. (d) What can you conclude from the results of (a), (b), and (c)?

So in this question, were given sample annual salaries in thousands of dollars and in part they were asked to find the sample mean and the sample standard deviation, which is given by this for Mila over here. So to find the sample mean and standard deviation, we basically use thes formulas. They substitute all the values of X, and our sample means is equal to 41 point 6923 thousands of dollars. Our sample standard deviation is 5.99 rounded to two decimal places. And so this is our answer to part in now for part B, we're told that each employing takes $1000 race. So you get $1000 races. Since all of these air in thousands of dollars, we're gonna add one. So the soldiers on 41 36 all the way up to 48 and then we're going to calculate our sample mean and standard deviation, for example, mean in this case is 42.6923 and our sample standard deviation actually stays the same at five point 99 Now, in part C, we're told that each employee takes a pay cut off $2000. So all of our values, you are going to decrease by two. So this is going to become 37 38 so on. And in that case, our sample mean is basically going to decrease by two from the initial. So we're gonna have 39.69 on our sample. Standard deviation remains the same at 5.99 So we have our answers to part A B and sink. Now let's move on to part Dean. So in part D were asked what we can conclude from the results of A, B and C So basically what? We can conclude this, that when we had or subtract a constant value from the data when we add or subtract a constant valley from our data, our mean well increase or decrease. Why the same amount So say we add or subtract an amount key from the data. Are minnow increase or decrease by the same amount? What the standard deviation remains the seen? Because the variation the data is constant. It just increases or decreases all the data just cool up or down by the same amount. So the standard deviation remains the same, but to me increases or decreases by the value that we had or subtract the data.

Welcome to New Madrid. This is another favorite problem of mine which actually gives a lot of good understanding to a student. So let me tell you what was the question. The question said that you have to multiply two with each of these values and then find the mean median mode and then come there. So what I did what I chose to do was to first offender real leadership. So the real leader said it would be this people see little of these values are obtained by multiplying. Yeah. So if you remember the formula of men would be so I will write X. One but because this is my ex one values and this is extra. So X one bar will be won by 14 because there are 14 values. Got it. So one by 14 the sum of all these values. So the sum of all this would be prime 075 Okay, so that gives us yeah it's 48.2 something critic. And then yes we look if you look at extra bar we'll have been won by 14. But this time we will be multiplying it. 181 finds you before we proceed and do the division. Look at this number and this number 75 develop disease that's here chaotic and then nine develop. This is this clearly this is nothing but getting doubled. So the final answer will also double and it will be 1 21. Yeah, 96 point four. All right. Now, if we look further, we have to find the model a more immediate media. So now the median we have the orders, data order data with us. If you see the reporting values of of course the seventh and the eighth value would be the average of these two values which will be 6 25. And here also this will be there mood. Why? Because there are $14 and this is 1234567 Which is important immediate. Which is another important 1, 1911, 12, 13 14. It's about a 14 7 and eight seventh value. Because sequences in by two and eight value and we take the thumb and divide by two. So I hear whatever values media that is also doubling from that value. Now, time for the mode support calculation. We can look at this data directory. So if you see 700 is a value that's occuring three times in the data, correct? At a stretch. No other when you work with more than that and if you see this side 1400. So if this is the mood so you're getting younger and this is going on 1400 then yes, even more than usual. So when there is a scale change, right? The previous, the new data is nothing but two times the old data than even means is two times the old mean the mood of the old new data is two times the mode of the previous data median of the new data is two times the median of the previous data. So I have also summarized this as a format about cable so that we can understand or visualize it better. So let's have a look so I don't worry about this tiny typing typing mistake from my end and what I meant over here he is. Let me show you the image and here it comes. If you see what we hear is stunning mistake is there? It should be too right. So that's a small thinking mistake. You can ignore it. If you see each of the values are doubled. The source reason, the main reason being that we already have it. Easy time stuff or variable. If that happens then central tendency also ships. So if there is any scale change or origin change of variable, then center central tendency of that available to be shifting. If there is an origin change or a scale shift, it will change. So if our data set expands like while multiplying with to the data set from this, it will go to this or you can do the opposite. Also, both cases, all the three measure of central tendencies will get impacted because they move along the room along with the radar set. So I hope I could explain this dream. You have any questions about.

Welcome to New Madrid. We have given the weekly salaries in dollars fought 14 workers. So in order to find the mean, the formula goes by expert equals to one by in submission. Excite items from guidance from 12 So here in is 14. We have won by 14 submission. I went from 1 to 14 submission. So this notation will mean we have to take some of all these values. I have already given that value ready for us and feet 90 So then leave from these observations on simplifying which it becomes six or 8.8. Thank you Books. That means on the basis of this given number of weekly salaries, the average would be around the center of these uh salaries would be 6 48 point That means while somebody asks, what are the salaries of 14 members Instead of telling individual entries, you can summarize them by just saying average of those workers is around 6 $48.2 a week. So I hope you could understand the explanation. Let me know if you have any doubt. Bye bye.


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