Statistics - I need help - anyone know how to do this? PLEASE.. I'm new at this..

[CountryWolf07]

I am taking a Statistics class this quarter, and I was wondering if anyone would be kind enough to help me figure out this problem? I am still learning, but I get lost pretty easily. I will be getting tutored sometime this week. Here it is:

A school system employs teachers at salaries between $30,000 and $60,000. The teachers' union and the school board are negotiating the form of next year's increase in the salary schedule. Supose that every teacher is given a flat $1000 raise.


a) How much will the mean salary increase? The median salary?

b) Will a flat $1000 raise increase the spread as measured by thed istance between the quartiles? Explain.

c) Will a flat $1000 raise increase the spread as measured by the standard deviation of the salaries? Explain.

Raising Pay: Suppose that the teachers in the previous question each recieve a 5% raise. The amount of the raise will vary from $1500 to $3000, depending on present salary. Will a 5% across-the-board raise increase the spread of the distribution as measured by the distance between the quartiles? Do you think it will increase the standard deviation? Explain.

[JenBKR]

Ugh, I don't miss statistics at all. I barely got through - never been very good at math. Let me think it out a little bit (first thing monday morning I'm not at my best).

Do you guys use SPSS? I don't miss that program either!

[Pembroke_Corgi]

Does the question give you any more information? Like, how many teachers are employed, and how much they each make?

The mean is the total salaries / by the number of salaries. For example, 30,000 + 40,000 + 60,000 = 130,000 / 3 = 43,333. The median is the middle number in an ordered data set. So with our example of 30,000 40,000 and 60,000, the median would be 40,000.

Quartiles divide the data by 25% each time. The 1st quartile (Q1) cuts off the first 25%, Q2 50%, and Q4 75%. The difference between the 1st and 3rd quartiles is called the interquartile range.

For example, let's use the numbers 1, 4, 6, 8, 10, 11, 13, 15, 20, 23

There are 10 numbers (in order), the 1st half (1-10) would be 50%, so that's Q2.

The median of 1-10 here is 6, so that is Q1.

The second half is numbers 11-23, and the median is 15, so this is Q3.

Q3 (15) - Q1 (6) = 9 Therefore, the interquartile range is 9.

You can apply this to your question by computing the interquartile range before the raise and after the raise.

Standard deviation is square root of the sum of deviations squared divided by (N-1). If there are 4 salaries of 30,000, 35,000, 40,000 and 60,000, we need to first find the mean. The mean would be 165,000 / 4 = 41,250.

I find that a chart helps with this.

Salary(x) - Mean (x bar) = x - mean squared

30,000 41,250 -11250 126,562,500

35,000 41,250 -6250 39,062,500

40,000 41,250 -1250 1,562,500

60,000 41,250 18750 351,562,500

sum of x - mean squared =

518,750,000

So we have 4 salaries, which makes N = 4, N-1 = 3,

so 518,750,000/3 = 172,916,666.67 the square root of this is 13,149.79, which would be our standard deviation.

All you need to do is plug in your salaries and do it before and after the raise. I would recommend using a computer because it is rather tedious and time consuming by hand, and it's easy to make simple errors. Hopefuly that helped instead of confused you further...if you give me the data you are working with I can help you some more. I haven't had stats in a while, but I actually did enjoy it as you can see.

Good luck!

[Iilo]

If you don't already have a TI-83 Graphing calculator, I'd suggest investing in one.

I'm taking an AP stat course right now, but I'm awful at explaining math through words, sorry.

Pembroke_Corgi gave you a lot of good information.

[caseysmom]

That was my least favorite subject in college!