Fall Semester 2002
You have 50 minutes. Please don't rush. Good luck and do well.
please calculate the mean and the median.
9, 3, 1, 7, 10
The sum of the numbers is 30 so the mean is 6. If you srot the numbers ascending you will find 7 is in the middle, so 7 is the median value.
1, 2, 3
Note: please make it clear how you calculate it.
The mean is 2, the deviations to the mean are -1, 0, and 1. The sum of these numbers squared is 2. The standard deviation will be the square root of 2 divided by n or n-1 depending on the definition you use.
how many of the scores are lower than 65?
Please express your answer as a percentage and justify your answer.
About 50-34 = 16% since 65 is exactly one standard deviation away from the mean.
In a normal distribution 50% of the scores are below the mean and 34% more are between the mean and the mean plus one standard deviation. That's 84%. 84% is exactly what we have below 145, so 145 must be exactly one standard deviation away from the mean. That makes the standard deviation about 145-120=25.
They're the same, since in both cases 75 has 84% of the scores in the distribution behind it. One can use z-scores also to obtain the same ordering information.
The s-zcores are equal so none of the scores is better than the other one.
Number of heads Frequency of occurrence 0 273 1 999 2 1490 3 996 4 241
Given these results, what's the estimated probability?
Experimentally 999/(273+999+1490+996+241) which is about 0.25