Math Exercises: Mathematical Statistics 
The twins Caroline and James have created a table of their school marks, which they got throughout the whole semester in certain subjects :
Calculate the final school mark of the twins in all subjects, if the range of the school marks is from 1 to 5.
The following table contains measured heights of 63 students with the corresponding counts of them :
Determine the arithmetic mean, median, mode, variance and a standard deviation of the student's height.
While weighing twenty of onekilogram sugar bags we noted the measured values in kg :
When measuring the heights of students in the class the measured values have been entered into the table (in cm). Calculate the median, mode and the arithmetic mean of student heights and add the relative frequencies of the students to the table.
We measured the height (value X) and the weight (value Y) of ten students; the values are shown in the table below. Find the arithmetic means and , fill in the table and determine the correlation coefficient between the measured height and weight of the students.
We measured the flat area of 30 apartments and we have measured the following values in m^{2} :
The electrical wiring requires cables with a high strength. We examined values for two types of cables :
The airline company estimates the average number of passengers. During the 20 days, the average number of passengers was 112 with the sample variance of 25. Find the 95% twosided confidence interval for the average number of passengers μ.
By measuring the resistance of the cable of eight randomly selected samples we obtained the following values: 0.139, 0.144, 0.139, 0.140, 0.136, 0.143, 0.141, 0.136. Suppose that the measured values can be seen as the realization of random sample from a normal distribution with the unknown mean and the unknown variance. Find the 95% confidence interval for the mean.
Let the systematic error of the measuring instrument be zero. Under the same conditions we performed ten independent measurements of one and the same quantity μ, where μ = 1,000 m. The measured data are given below :
Find the 90% confidence interval for the standard deviation σ.
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