help homework dont know how to do it could someone explain it please

[amd4lif3]

simply i have no idea how to do the last queston in my work i dont want anyone to work it out for me, i would like guidence of how to tackle the queston pleaseeeeee

The data for one class of 20 students is listed below as a percentage to two significant figures..
76, 77, 78, 79,81, 81, 82, 83, 84, 80, 79. 80, 80, 80, 80,79, 79, 78, 80, 78.
The central limits theory suggests that, distribution of a set of sample means is normal. Calculate the mean and standard deviation for this data and test how close it is to a normal distribution.

 

[PapaWood]

Mean = average. Sounds like thats what you are looking for, you add all those numbers together, take that number and divide it by how many numbers you added up. so lets say 10, 9, 9, 10, 3 gives me a mean of 8.2

Hope that helps.

 

[PapaWood]

The Standard Deviation is a measure of how spread out numbers are.

 

[noreaster]

The mean is easy to calculate, simply sum all of the data points then divide by the number of data points, in this case:
(76+77+78+...+80+78)/20=mean
The standard deviation for this set (discrete random variables...student's score) is the square root of the sum of each data point minus the mean squared divided by the number of data points, in this case:
(((79-mean)^2+(77-mean)^2+...+(78-mean)^2)/20)^(1/2)=standard deviation

Then use the central limit theory to determine how close the mean and standard deviation of this set is compared to a normally distributed set in this range.

 

[amd4lif3]

i have calculated the mean and standard deviation but do not understand how i can test to see how close it is to a normal distribution

 

[noreaster]

From Wikipedia:

More precisely, it states that as n gets larger, the distribution of the difference between the sample average Sn and its limit µ, when multiplied by the factor √n (that is √n(Sn − µ)), approximates the normal distribution with mean 0 and variance σ^2.

Which to me would mean:
√20(SampleMean − NormalMean)
This yields a number, I cannot recall what it specifically represents, but I do know that the smaller the number the closer to normal your sample is (if SampleMean=NormalMean then the number would be 0). Sorry, I am a bit rusty on this but I hope this has helped some.

 

[srobin]

a normal distribution will look like a bell curve. mean is the average and standard deviation is the distance from the mean.

mean = Add up the number and divide my the number
SD = square root of the mean

Check out khan Academy.
https://www.khanacademy.org/math/probability/descriptive-statistics/variance_std_deviation/e/standard_deviation_of_a_population