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Work procedure and data processing. Having carried out multiple measurements of quantity t, it is also possible to draw a histogram for measured values and to verify a hypothesis about normal
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Having carried out multiple measurements of quantity t, it is also possible to draw a histogram for measured values and to verify a hypothesis about normal distribution, i.e. to find out, whether the measured values correspond to law of normal distribution described by Gaussian formula.
1. Drawing a histogram.
1.1. Deviate the pendulum by 3o … 5o angle and let it off. When the pendulum is in one of the extreme positions, turn on a time measuring device and measure the time of five complete oscillations. Perform the actions 50 times. Enter the results of measurement into the second column of table 5.3.
Table 5.3
| Measurement No. | Measured values ti, s | Measured values in ascending order ti, s | Intervals boundary t 01 – t 02, … t 0 i – t 0 k , | Number of values in interval D nk | 
|
| … … … | |||||
1.2. Analyse the obtained values and arrange them in increasing progression starting from the smallest value tmin up to the largest value tmax. Enter arranged values into the third column of the table.
1.3. Divide the full range of the measured values into 5 equal intervals D t and determine boundary values t 0 of each interval in the fourth column (t 01= tmin +D t; t 02= t 01+D t etc.). Separate the values ti which are relevant to boundary values by horizontal line in the table.
1.4. Count a number of values D ni which has been included in each interval and enter it into the fifth column. Calculate the rate of reappearance of the measured values D n i/ n. Enter the obtained results into the sixth column.
1.4. Draw the histogram of the measured values using as an example the theoretical diagram.
2. Determination of gravity acceleration.
2.1. Find in the histogram the interval with the greatest rate of reappearance of the measured values.
2.2. Calculate the average mean of measured values which are contained within the interval.
2.3. Using expression (5.7) determine the value of gravity acceleration.
2.4. Deduce an equation for calculation of the error of indirect measurement of gravity acceleration.