The following is the total list of grades of students who have taken an
upper division laboratory course over the last few years. The lowest grades are generally
from students who do not do all the work required and/or do not hand in the assignments on
time. Note that this behavior generally does not result in a symmetric distribution for a
small number of students (in the limit of a large number of students this distribution
would be bimodal).
A). Find the mean, median, most probable value, and standard
deviation of this distribution of 40 grades. Quote your results to two significant
figures. You may perform the calculation by hand, write your own program, or use a
software package (such as Excel) to do the calculations for you, but you must show your
work by explaining how you would calculate each quantity.
B). Make a histogram of the data by dividing up the possible grade
in bins of 5 and plotting the number of students who received a grade in that range.
Here's an ASCII list of the same data below.
Student |
Grade |
Student |
Grade |
Student |
Grade |
1 |
70 |
15 |
93 |
29 |
43 |
2 |
52 |
16 |
54 |
30 |
55 |
3 |
71 |
17 |
52 |
31 |
87 |
4 |
62 |
18 |
61 |
32 |
49 |
5 |
61 |
19 |
72 |
33 |
92 |
6 |
97 |
20 |
67 |
34 |
64 |
7 |
54 |
21 |
74 |
35 |
80 |
8 |
68 |
22 |
73 |
36 |
56 |
9 |
81 |
23 |
61 |
37 |
89 |
10 |
85 |
24 |
53 |
38 |
43 |
11 |
70 |
25 |
80 |
39 |
71 |
12 |
97 |
26 |
73 |
40 |
62 |
13 |
79 |
27 |
49 |
||
14 |
82 |
28 |
99 |