Question 480840: Can you please help me to come up with a formula for transmuting raw scores into percentages the conditions are :(lowest possible score is zero and its equivalent is 65% and the highest possible score is 100 and its equivalent is 97 % only. using excel formulas please!!! thank you.)
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 0 is equivalent to 65%
100 is equivalent to 97%
the range from low to high in the raw scores is 100 points.
the range from low to high in the percent scores is 32%
32% / 100 = .32%
your equation would be:
percent score = .32% * raw score + 65%
the table would look like this:
raw score
percent score rounded to nearest 100th of a percent
percent score rounded to nearest 10th of a percent
percent score rounded to nearest percent
0 65.00% 65.0% 65%
1 65.32% 65.3% 65%
2 65.64% 65.6% 66%
3 65.96% 66.0% 66%
4 66.28% 66.3% 66%
5 66.60% 66.6% 67%
6 66.92% 66.9% 67%
7 67.24% 67.2% 67%
8 67.56% 67.6% 68%
9 67.88% 67.9% 68%
10 68.20% 68.2% 68%
11 68.52% 68.5% 69%
12 68.84% 68.8% 69%
13 69.16% 69.2% 69%
14 69.48% 69.5% 69%
15 69.80% 69.8% 70%
16 70.12% 70.1% 70%
17 70.44% 70.4% 70%
18 70.76% 70.8% 71%
19 71.08% 71.1% 71%
20 71.40% 71.4% 71%
21 71.72% 71.7% 72%
22 72.04% 72.0% 72%
23 72.36% 72.4% 72%
24 72.68% 72.7% 73%
25 73.00% 73.0% 73%
26 73.32% 73.3% 73%
27 73.64% 73.6% 74%
28 73.96% 74.0% 74%
29 74.28% 74.3% 74%
30 74.60% 74.6% 75%
31 74.92% 74.9% 75%
32 75.24% 75.2% 75%
33 75.56% 75.6% 76%
34 75.88% 75.9% 76%
35 76.20% 76.2% 76%
36 76.52% 76.5% 77%
37 76.84% 76.8% 77%
38 77.16% 77.2% 77%
39 77.48% 77.5% 77%
40 77.80% 77.8% 78%
41 78.12% 78.1% 78%
42 78.44% 78.4% 78%
43 78.76% 78.8% 79%
44 79.08% 79.1% 79%
45 79.40% 79.4% 79%
46 79.72% 79.7% 80%
47 80.04% 80.0% 80%
48 80.36% 80.4% 80%
49 80.68% 80.7% 81%
50 81.00% 81.0% 81%
51 81.32% 81.3% 81%
52 81.64% 81.6% 82%
53 81.96% 82.0% 82%
54 82.28% 82.3% 82%
55 82.60% 82.6% 83%
56 82.92% 82.9% 83%
57 83.24% 83.2% 83%
58 83.56% 83.6% 84%
59 83.88% 83.9% 84%
60 84.20% 84.2% 84%
61 84.52% 84.5% 85%
62 84.84% 84.8% 85%
63 85.16% 85.2% 85%
64 85.48% 85.5% 85%
65 85.80% 85.8% 86%
66 86.12% 86.1% 86%
67 86.44% 86.4% 86%
68 86.76% 86.8% 87%
69 87.08% 87.1% 87%
70 87.40% 87.4% 87%
71 87.72% 87.7% 88%
72 88.04% 88.0% 88%
73 88.36% 88.4% 88%
74 88.68% 88.7% 89%
75 89.00% 89.0% 89%
76 89.32% 89.3% 89%
77 89.64% 89.6% 90%
78 89.96% 90.0% 90%
79 90.28% 90.3% 90%
80 90.60% 90.6% 91%
81 90.92% 90.9% 91%
82 91.24% 91.2% 91%
83 91.56% 91.6% 92%
84 91.88% 91.9% 92%
85 92.20% 92.2% 92%
86 92.52% 92.5% 93%
87 92.84% 92.8% 93%
88 93.16% 93.2% 93%
89 93.48% 93.5% 93%
90 93.80% 93.8% 94%
91 94.12% 94.1% 94%
92 94.44% 94.4% 94%
93 94.76% 94.8% 95%
94 95.08% 95.1% 95%
95 95.40% 95.4% 95%
96 95.72% 95.7% 96%
97 96.04% 96.0% 96%
98 96.36% 96.4% 96%
99 96.68% 96.7% 97%
100 97.00% 97.0% 97%
the first column is the raw score.
the second column is the percent score rounded to the nearest 100th of a percent.
the third column is the percent score rounded to the nearest 10th of a percent.
the fourth column is the percent score rounded to the nearest percent.
it appears that rounding to the nearest 10th of a percent is as rounded as you want to go in order to differentiate between raw scores.
if you want to group raw scores, then rounding to the nearest percent would be a way of doing it.
for example, anybody who got 96 or 97 or 98 right would get a 96%, and anybody who got 99 or 100 right would get 97%.
this is not weighted in any way.
it assumes that each point in the raw score has equal weight in the final score.
there is compression, but that's necessary when you're trying to fit 100 points into 32 percentage points.
|
|
|
