M.Phil. Physics (Third Semester)
Course: Simulation in Statistical Physics
Home Work # 2
Due Date: One week from today
(1) The distribution of the diameters of heads of pins (total = 250) manufactured by a
company are given here. First find mean, median and mode. Then compute the
variance and standard deviation.
Diameter (mm)
Frequency
7.247 โ 7.249
2
7.250 โ 7.252
6
7.253 โ 7.255
8
7.256 โ 7.258
15
7.259 โ 7.261
42
7.262 โ 7.264
68
7.265 โ 7.267
48
7.268 โ 7.270
25
7.271 โ 7.273
18
7.274 โ 7.276
12
7.277 โ 7.279
4
7.280 โ 7.282
1
(2) Compute the second and third moments as well for the above problem.
(3) Draw a graph for above experimental distribution. Convert the variable (x) in
above table into standardized variable and then find the experimental probability
for each class. Finally, compute probability from a Normal distribution having
same mean and standard-deviation. Compare results using chi-square test.
(4) Find the relative dispersion and coefficient of variation. Then compute 10-90
percentiles for above distribution. Comment on answers.
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