Question 1210327: YyThe data represent the scores obtained by 9 applicants in an interview arranged in
ascending order: (3x+2), 22, (4x-2), 23, 25, (5x-4), 29, 29 and (x²-7).
(a) Given that the range is 9, find the
(i) value of .x;
(ii) mean mark of the applicants.
(b) If four of the applicants who obtained the highest score were selected, determine the
pass mark.
Found 2 solutions by mccravyedwin, greenestamps:
Answer by mccravyedwin(405)   (Show Source):
You can put this solution on YOUR website!
The mean is
The range is
x=6; x=-3.
scores aren't negative, so x = 6
The mean is 
So the scores are:
3x+2 = 3(6)+2 = 18+2 = 20
22 = 22
4x-2 = 4(6)-2 = 24-2 = 22
23 = 23
25 = 25
5x-4 = 5(6)-4 = 30-4 = 26
29 = 29
29 = 29
x2-7 = (6)2-7 = 36-7 = 29
So they are in non-descending order, not ascending order, as stated.
Since the top 4 scores are 29, 29, 29, 26, all passed, and the applicant
with 25 failed, the pass mark had to be 26, assuming it had to be a whole
number.
Edwin
Answer by greenestamps(13195)  (Show Source):
You can put this solution on YOUR website!
Start using the given information that the range is 9.
x = 6 or x = -3
But negative scores don't make sense, so x is 6. The scores are then
20, 22, 22, 23, 25, 26, 29, 29, and 29
The mean of the marks can of course be found by adding the 9 scores and dividing by 9.
But when finding the mean of a set of numbers that are all close together, another method is to guess the mean and look at the "overs" and "unders" compared to that guess.
Looking at the scores, it looks as if the mean is about 25. Comparing the 9 scores to that guess, we get
-5, -3, -3, -2, 0, 1, 4, 4, and 4
Adding those gives us -13+13 = 0, so in fact our guess of 25 for the mean is correct.
ANSWERS:
(a)(i) x = 6
(a)(ii) the mean score is 25
(b) the top 4 scores are 26, 29, 29, and 29, so the pass mark is 26
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