Question

Independent observations of the random X magnitude, which characterizes the deviation of the length of the part from the required technical conditions, are presented in the form of a simple statistical series. It is necessary to build a statistical (variation) series and histogram, to find estimates for mathematical expectation and variance.

Show your work.

1	4. 1
2	4. 6
3	4. 63
4	4. 94
5	5. 12
6	4. 12
7	4. 27
8	5. 17
9	5. 03
10	5
11	4. 29
12	4. 31
13	4. 42
14	4. 67
15	4. 54
16	4. 82
17	4. 38
18	4
19	5.21
20	5.22
21	3.94
22	3.8
23	3.72

Answer 1

Expectation and variance from Histogram:

Now estimate the expectation:

Now calculate

Now estimate the variance :

Yes, It is necessary to build a statistical (variation) series and histogram to estimate the expectation and variance.

Here statistical (variation) series means to arrange data in asscending order.