Intermediate Quantum 491: Homework 1 Solutions

1-1

Consider the sets of test grades gi = 75.71 71.43 41.43 64.29 77.14 65.7158.57 68.57 24.29 54.29 48.57 68.57 78.57 61.43 58.57

Then we get the mean = 61.1, STD = 14.6.

Figure 1: Histogram of data with 10 bins from 0 to 100: 〈x〉 = 60.3 ∆x = 14.1

Let bin centers be x[i] and number in each bin n[i] with∑

n[i] = Nthe total number of grades.

Then mean

〈x〉 =

∑n[i]x[i]

N

and variance

(∆x)2 =

∑n[i](x[i]− 〈x〉)2

N − 1

Where we divide by N-1 because we used the data to calculate themean.

The probability to have a grade in the ith bin is estimated from thisdata as p[i] = n[i]/N .

Michael Gold

(1.4)

Michael Gold

(1.6)

Michael Gold

(8) (1.12)