can statistics prove results of standardized test?

@acudavid Said

Hi, I'm a beginner with statistics and need help. I have data for the percentage of test-takers who took a state standardized test. The results range from 47% to 68% of the students passing in each of the last 20 times the test was given, and each iteration is for about 700 test-takers (low just under 500 and high just above 1000, random size population & students had equivalent education) Just for comparison, a similar test--a national standardized test-- has results that range from 70% to 75% passing. (the range is narrower) I am wondering about the range of the state test, if it abnormal for a standardized test to have the passing percentage vary by 21%.
I plugged numbers into an online calculator and don't know if they are correct, or what they mean.
Number of samples 20
Mean 56.55
standard deviation 6.56526
Variance (std deviation) 43.10263
Population (std deviation) 6.39902
Variance (pop std dev) 40.9475
Value 48
z-score -1.30230943

I seem to remember that if a standard deviation is > 10% of the Mean, that reflects poorly on the results, and if a result is more than one standard deviation away, it is statistically significant, but I am not sure. Please help. I have to decide if I am going to challenge the results.
The state test is scored with a criterion referenced scoring system, which is a pass/fail system, where a passing score is determined. It is kind of like the way a jury deliberates, but what they do is decide how hard each question is and rate it, and average the values, and that is the passing score. I think this is inherently subjective.
(the national test uses a preset score of 70, so 70% is passing and 69% is failing. The state test passpoints range from 65 to 75% in our 20 iterations)
In the 2nd to last iteration the state-test passpoint was set at 118 correct out of 175 and 66% of the students passed, while the last iteration was set at 132 of 175 with 48% passing.
Here are the last 20 iteration--in case I calculated wrong:
48,59,61,61,53,61,53,66,58,57,68,66,47,49,50,65,53 ,54,51,51
Thank you