Procedure
1. Flip the coins (not less than 20) and count the number of dropped arms. Repeat 50 times. The counts recorded in the Table # 2.
Table # 2 The number of dropped arms
№ |
xi |
xi |
xi2 |
№
|
xi |
xi |
xi2 |
№
|
xi |
xi |
xi2 |
1 2 . . . 15 |
|
|
|
16 . . . . 25 |
|
|
|
35 . . . . 50 |
|
|
|
2. Calculate the arithmetic mean value х of all results.
3. Calculate the deviation of individual measurements хi and their squares хi2, to make them in the same table.
4. Calculate the mean square error of the individual measurement result by the formula (3). Calculated by the formula (10) the mean square error of the arithmetic mean.
5. Define хmin and хmax,, divide this period into intervals and number them.
6. Determine to which interval refers individual measurement.
7. Sum the number of measurements (ni), falling in each interval, write these numbers in Table 3.
8. Construct a histogram.
9. Construct the reduced histogram.
10.
Calculate
the
value
of
the
probability density function
for
values
,
where
j-
number
the
interval
i.e.
to
the
middle of each
interval,
and
write
these
values in
the
last
table.
Table # 3 The data for the histogram and the Gaussian curve
Number of interval (j): j=1…k |
ni |
|
|
|
e- |
f(x) |
1 2 . |
|
|
|
|
|
|
11. Construct a Gaussian curve on the graph where you construct a reduced histogram.
12. Calculate the confidence interval for a given instructor reliability and record the final result according to formula (12). By formula (13) calculate the relative error of the experiment.
Control questions
Define absolute and relative errors. 2. How are the errors classified by the properties? 3. What are the properties of normal distribution of random errors? 4. What reliability corresponds to the standard deviation? 5. Which of two (1> 2) has more high-quality measurement?