Help with standard deviations, means, distributions
I am confused about comparing data by looking at the mean and standard deviation.
Example shows that Group A (don't know the population) does a test and has the mean of 100 out of 120. Group A has a standard deviation of 5.
Group B (don't know the population) does a test and has the mean of 85 out of 120. Group B has a standard deviation of 10.
A person does the same test and scores 90 out of 120.
Could I assume that both Group A and Group B data are normally distributed?
Also, how would i see if the person did well compared to Group A and Group B? What is the way of comparing?
Thank you for the help.
The Given person is not from either group.
Under the circumstances the person's score has no bearing on the distribution.
The deviations are defined by assuming Normal distribution.
Therefore, considering normal distribution the Group A with standard deviation 5 has most values between 95 and 105.
Group B with standard deviation of 10 has values from 75 to 95.
Therefore the person at score of 90 is out of range for Group A and has done poorly compared to Group A. But he has done as well as members of Group B and bettr marks than the average of Group B.
The mean 100 out of 120 with SD=5 means that in general the variabilities of data in the population is 100 + or - 5. Thus, data in this population range from 95 - 105.
The mean 85 out of 120 means that in general the variabilities of data in the population is 85 + or - 10. Thus, data in this population range from 75 - 95
In group A, from the question we know that there is a person score 90 out of 120. It means that there is a score that not in the range 95 - 105. This data is an outlier. Data with an outlier cannot have a normal distribution.
There is not enough information to make a decision about distribution in group B. However, if assumed that the case of this person is turn into group B. We can see that the 90 out of 120 is in the range of 95 - 105. Thus, data in group B has a normal distribution.
If a person reach 90 out of 120 in group A, it means that this person did worse on the test, because his/her score falled into lower than the lowest average, which is 95. However, if this person is in group B, he/she did fair on the test because his/hert grade is in the mid of range 95 - 105.
I hope this answer can help you.