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Math Exercises & Math Problems: Mathematical Statistics

 

 

 

 

1. The twins Caroline and James have created a table of their school marks, which they got throughout the whole semester in certain subjects :

 

Mathematical statistics - Exercise 1

 

Calculate the final school mark of the twins in all subjects, if the range of the school marks is from 1 to 5.
In how many subjects will Caroline get better mark on the report card than her brother James ?

 

2. The following table contains measured heights of 63 students with the corresponding counts of them :

 

Mathematical statistics - Exercise 2

 

Determine the arithmetic mean, median, mode, variance and a standard deviation of the student's height.

 

3. While weighing twenty of one-kilogram sugar bags we noted the measured values in kg :
1.00, 1.01, 1.05, 0.99, 0.95, 1.00, 0.98, 0.99, 1.04, 1.06, 0.93, 1.00, 1.03, 0.97, 1.00, 0.99, 1.05, 1.01, 0.94, 1.00.
Determine the median and the variance of the measured weight.

 

4. 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.

 

Mathematical statistics - Exercise 4

 

5. 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 Arithmetic mean of the measured heights and Arithmetic mean of the measured weights, fill in the table and determine the correlation coefficient between the measured height and weight of the students.

 

Mathematical statistics - Exercise 5

 

6. We measured the flat area of 30 apartments and we have measured the following values in m2 :
82.6, 57.3, 70.4, 65, 48.4, 103.8, 73.6, 43.5, 66.1, 93, 52.6, 70, 84.2, 55, 81.3, 61.5, 75.1, 34.8, 62.4, 116, 70.1, 63.6, 93, 59.2, 65.9, 77.2, 52.8, 68.7, 79.2, 87.4.
a) Create a table of grouped frequency distribution for the number of classes k = 9.
b) Construct a histogram of relative frequencies of the flat areas.
c) From the specified values estimate the sample mean and the variance.
d) From the middle values of the intervals and from their frequencies estimate the sample mean and the variance.

 

7. The electrical wiring requires cables with a high strength. We examined values for two types of cables :
1st type: 302, 310, 312, 310, 313, 318, 305, 309, 301, 309, 310, 307, 313, 229, 315, 312, 310, 308, 314, 333, 305, 310, 309, 314
2nd type: 300, 310, 320, 309, 312, 311, 315, 317, 309, 313, 315, 314, 307, 322, 313, 313, 311, 316, 31, 314, 308, 319, 313, 312
Estimate the mean of the strength of both types of cable using the sample mean, median and the mode.

 

8. 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% two-sided confidence interval for the average number of passengers μ.

 

9. 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.

 

10. 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 :

 

Mathematical statistics - Exercise 10

 

Find the 90% confidence interval for the standard deviation σ.

 

 

 

 

 

 

You might be also interested in:

- Probability

- Variations, Permutations, Combinations

- Factorials and Combinatorial Expressions

- Combinatorial Equations and Inequalities

 

 
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