Question:
The 10 students in a history class recently took an examination. What was the maximum score on the examination?
(1) The mean of the scores was 75.
(2) The standard deviation of the scores was 5.
Quote
Hi
VeritasKarishmaI have a question. If I were to obtain the maximum possible score with this SD, I would consider for a set of values with all equal to mean except 2 to meet the SD Criteria.
For eg. {75,75,...75, x, y}
This is because I would like to use the SD between x and y and keep x, y equidistant from the mean 75, so that the mean of the whole set is maintained.
In that case I will get by SD formula 5^2 = {0+0+0+0+..+(x-75)^2 + (y-75)^2}/10
Since i take distance of x from mean = distance of y from mean to maintain set mean
i get (x-75)^2 = (y-75)^2 = 2(x-75)^2
Therefore 250= 2(x-75)^2
x-75 = Root(125)
x = 75+/- 5Root(5). = 86.18 and 63.81
I suppose this is the maximum "possible" value for x ?
Is there a difference between max "possible" value for x and maximum value of x.
Since maximum value of x will vary by sets {different sets will have their own maximas} but maximum possible value will not.
I say C. Why E ?
Kindly help clear if i am wrong.