Research math question

[librarygirl]

Online Masters Research class requires me to answer math problems. Im lost. Teacher suggested find a high school teacher to help, but I dont know any high school math teachers.

I know that mean is adding all the numbers together and dividing, median is the one in the middle. But I can only find them if I have a set of numbers. I am completely lost at this stuff.

Can you help?:

Given a normal distribution with a mean of 75 and a standard deviation of 5, answer the following questions:

What is the approximate value of the median? It would be the number in the middle, but I dont have an idea of how to find that.

What percentage of scores fall between 70 and 75?

What percentage of the scores would lie between two standard deviations below and two standard deviations above the mean?

 

[galactus]

Online Masters Research class requires me to answer math problems. Im lost. Teacher suggested find a high school teacher to help, but I dont know any high school math teachers.

I know that mean is adding all the numbers together and dividing, median is the one in the middle. But I can only find them if I have a set of numbers. I am completely lost at this stuff.

Can you help?:

Given a normal distribution with a mean of 75 and a standard deviation of 5, answer the following questions:

What is the approximate value of the median? It would be the number in the middle, but I dont have an idea of how to find that.

For a normal distribution, the mean and median are the same thing. In this case, 75.

What percentage of scores fall between 70 and 75?

This is a normal distribution. The Empirical Rule (also called the 68-95-99.7 Rule) states that about 68% of the data falls within one standard deviation above and below the mean. Since the mean is 75 and the standard deviation is 5, that means about 68% of the data falls between
75-5=70 and 75+5=80
So, half of 68% is 34%. That is the percentage of the data that falls one standard deviation below the mean, or between 70 and 75.
I have posted a graph of the normal distribution curve. Also, known as the Bell curve.

On the graph, in this case, \(\displaystyle {\mu}=75, \;\ {\sigma}=5\)

What percentage of the scores would lie between two standard deviations below and two standard deviations above the mean?

The Empirical Rule says that about 95% of the data falls within 2 standard deviations above and below the mean. So, 95% of the data will range between 75-2(5)=65 and 75+2(5)=85.

This is the simplest way to look at it. To do it more precisely, we can use what is known as a z-score, but that is not really necessary in this case.

To find the percentage of data that falls between 70 and 75, we can use \(\displaystyle z=\frac{x-\mu}{\sigma}\)

\(\displaystyle z=\frac{75-75}{5}=0\)

\(\displaystyle z=\frac{70-75}{5}=-1\)

The 0 means we are right in the center on the mean. The -1 means we are 1 standard deviation below the mean.

Look these values up in a z table and we see that 0 corresponds to a z score of .5 and -1 corresponds to a z score of .1587

Subtract them and we get .5-.1587=.3413.

34.13%of the data falls between 70 and 75. Close enough to 34% the Empirical tells us.

 

[librarygirl]

That makes sense that the mean and median would be the same thing. Thanks for all of your help. I know that research is all about numbers, but you would think there would be a seperate class on it for the program since its so difficult to do. Thats a lot of terms and technology. Im glad theres some wonderful math minded people to help us that arent. Thanks again!