Statistics

2010013501

Level: 
A
Two years ago, a family business reported gross profit of \(3.5\) million euros. During the pandemic, the company got into trouble so that its last year gross profit fell by \(20\%\) and its gross profit of this year was \(1\) million euros lower than of the last year. What was the average annual decrease in the gross profit reported by the company during the priod under review? Round the result to the tenth of a percent.
\(28.3\%\)
\(27.9\%\)
\(26.7\%\)
\(28.2\%\)

2010013502

Level: 
A
The annual production of a business is recorded in the following table. Find the compound annual rate of decline in production for a given period \( 2017 \) - \( 2020 \). (I.e., the average annual coefficient of the production decline, i.e., the ratio that provides a constant decline rate over the time period.) Round the result to four decimal places. \[ \begin{array}{|c|c|c|c|c|} \hline \text{Year} & 2017 & 2018 & 2019 & 2020 \\\hline \text{Production (pcs)} & 55\: 000 & 50\: 000& 47\: 000 & 45\: 000 \\\hline \end{array}\]
\( 0.9353 \)
\( 0.9225 \)
\( 0.9898 \)
\( 0.9535 \)

2010013503

Level: 
A
Four seamstresses sew doll dresses in a sheltered workshop. During the six-hour working hours, the first seamstress sewed \(4\) dresses, the second \(5\), the third \(7\) and the fourth \(4\) dresses. What was the average time needed to sew one dress on this day?
\( 1\,\mathrm{h}\ 12\,\mathrm{min} \)
\( 1\,\mathrm{h}\ 20\,\mathrm{min} \)
\( 1\,\mathrm{h}\ 10\,\mathrm{min} \)
\( 1\,\mathrm{h}\ 24\,\mathrm{min} \)

2010013504

Level: 
A
The average price of a pork meat increased by \(15\%\) in the year \(2018\), by \(13\%\) in the year \(2019\) and by \(28\%\) in the year \(2020\). Find the average percentage growth of the price of the pork meat per one year in the period \(2017\)-\(2020\). Round your result to the nearest percent.
\(18\%\)
\(19\%\)
\(20\%\)
\(17\%\)

2010018101

Level: 
A
Andrea took part in a children's cycling race. The first part of the route led from the Lower Square to the Upper Square and Andrea completed it with an average speed of \(10\,\mathrm{km/h}\). Returning from the Upper Square to the Lower Square she rode the same route with an average speed of \(13\,\mathrm{km/h}\). We are interested in her average speed during the whole race. What type of average do we need to use?
Harmonic mean
Arithmetic mean
Geometric mean
Weighted arithmetic mean

2010018102

Level: 
A
The same component is manufactured simultaneously on two differently powerful machines. The first one makes \(1\) component in \(20\) minutes, the second one makes the same component in \(10\) minutes. We are interested in how long it takes on average to produce \(1\) component using these two machines. What type of average do we use for the calculation?
Harmonic mean
Geometric mean
Arithmetic mean
Weighted arithmetic mean

2010018103

Level: 
A
In February 2021, Aneta recorded an outdoor temperature in Ostrava-Poruba, always measured at \(2\) p.m. The results in \(^{\circ}\mathrm{C}\) are shown in the following table: \[ \begin{array}{|l|c|c|c|c|c|c|c|c|} \hline \text{Day} & 1. & 2. & 3. & 4. & 5. & 6. & 7. & 8. \\\hline \text{Temperature }(^{\circ}\mathrm{C}) & -1 & 3 & 7& 8 & 3 & 0 & -4 & -5 \\\hline \\\hline \text{Day} & 9. & 10. & 11. & 12. & 13. & 14. & 15. & 16.\\\hline \text{Temperature } (^{\circ}\mathrm{C}) & -4 & -3 & -6 & -4 & -3 & 2 & -2 & 0\\\hline \\\hline \text{Day} & 17. & 18. & 19. & 20. & 21. & 22. & 23. & 24. \\\hline \text{Temperature } (^{\circ}\mathrm{C}) & 3 & 8 & 4 & 5 & 5 & 8 & 5 & 16 \\\hline \\\hline \text{Day} & 25. & 26. & 27. & 28. & & & & \\\hline \text{Temperature } (^{\circ}\mathrm{C}) & 15 & 15 & 6 & 8 & & & & \\\hline \end{array} \] Determine the mode of the recorded temperatures.
\(8\,^{\circ}\mathrm{C}\)
\(3\,^{\circ}\mathrm{C}\)
\(-3\,^{\circ}\mathrm{C}\)
\(-4\,^{\circ}\mathrm{C}\)

9000139501

Level: 
A
Ten apples in a box have average mass \(200\, \mathrm{g}\). We remove one apple of the mass \(200\, \mathrm{g}\) from the box. What is the change in the average mass of the apples from the box?
The average mass of the apples does not change.
The average mass of the apples decreases by \(20\, \mathrm{g}\).
The average mass of the apples increases by \(20\, \mathrm{g}\).
There is not enough information to solve this problem.