Statistics

1003123503

Level: 
A
It is known that in the given time period one up to five pieces of the same product were sold in each of the 100 monitored shops. One piece was sold in \( 26 \) shops, \( 2 \) pieces in \( 64 \) shops, \( 3 \) pieces in \( 7 \) shops, \( 4 \) pieces in \( 2 \) shops and \( 5 \) pieces in one shop. How many pieces of the product were sold most frequently in the given shops? Choose the correct characteristic and its value.
Mode: \( 2 \) pieces
Arithmetic mean: \( 3 \) pieces
Median: \( 2 \) pieces
Median: \( 3 \) pieces
(Weighted) arithmetic mean: \( 1.88 \) pieces

1003123502

Level: 
A
At a weather station in Las Vegas temperature was measured every day at \( 7 \)pm during one month. The results are specified in the following table. \[ \begin{array}{|l|c|c|c|c|c|c|c|c|} \hline \text{Day} & 1. & 2. & 3. & 4. & 5. & 6. & 7. & 8. \\\hline \text{Temperature }(^{\circ}\mathrm{C}) & 24 & 22 & 21 & 26 & 22 & 23 & 21 & 23 \\\hline \\\hline \text{Day} & 9. & 10. & 11. & 12. & 13. & 14. & 15. & \\\hline \text{Temperature } (^{\circ}\mathrm{C}) & 21 & 26 & 20 & 23 & 24 & 19 & 21 & \\\hline \\\hline \text{Day} & 16. & 17. & 18. & 19. & 20. & 21. & 22. & 23. \\\hline \text{Temperature } (^{\circ}\mathrm{C}) & 21 & 20 & 26 & 23 & 24 & 22 & 23 & 26 \\\hline \\\hline \text{Day} & 24. & 25. & 26. & 27. & 28. & 29. & 30. & \\\hline \text{Temperature } (^{\circ}\mathrm{C}) & 25 & 23 & 22 & 25 & 27 & 26 & 22 & \\\hline \end{array} \] Determine the mode of the recorded temperatures.
\( 23 \,^{\circ}\mathrm{C} \)
\( 22\,^{\circ}\mathrm{C} \)
\( 21\,^{\circ}\mathrm{C} \)
\( 26\,^{\circ}\mathrm{C} \)
\( 21\,^{\circ}\mathrm{C} \) also \( 22\,^{\circ}\mathrm{C}\) also \(26\,^{\circ}\mathrm{C}\)

1003123501

Level: 
A
At a weather station in Las Vegas wind speeds were measured every day at \( 7 \)pm during one month. The results are specified in the following table. \[ \begin{array}{|l|c|c|c|c|c|c|c|c|} \hline \text{Day} & 1. & 2. & 3. & 4. & 5. & 6. & 7. & 8. \\\hline \text{Wind} (\mathrm{mps}) & 3 & 2 & 1 & 1 & 2 & 2 & 1 & 3 \\\hline \\\hline \text{Day} & 9. & 10. & 11. & 12. & 13. & 14. & 15. & \\\hline \text{Wind} (\mathrm{mps}) & 2 & 1 & 2 & 2 & 4 & 2 & 4 & \\\hline \\\hline \text{Day} & 16. & 17. & 18. & 19. & 20. & 21. & 22. & 23. \\\hline \text{Wind} (\mathrm{mps}) & 4 & 2 & 2 & 3 & 2 & 12 & 13 & 6 \\\hline \\\hline \text{Day} & 24. & 25. & 26. & 27. & 28. & 29. & 30. & \\\hline \text{Wind} (\mathrm{mps}) & 5 & 7 & 2 & 3 & 8 & 9 & 12 & \\\hline\end{array} \] Determine the median of the recorded wind speeds.
\( 2{.}5\,\mathrm{m/s} \)
\( 2\,\mathrm{m/s} \)
\( 4\,\mathrm{m/s} \)
\( 6\,\mathrm{m/s} \)

1003029508

Level: 
A
There were the following speeds of six cars recorded on one of the roads in New York: $66\,\mathrm{mph}$, $57\,\mathrm{mph}$, $71\,\mathrm{mph}$, $54\,\mathrm{mph}$, $69\,\mathrm{mph}$, $58\,\mathrm{mph}$. We would like to know the average of these recorded speeds. What type of average do we need to use?
Arithmetic mean
Geometric mean
Harmonic mean
Weighted harmonic mean

1003029507

Level: 
A
You recorded the outdoor temperature in the place of your residence at the noontime during the past ten consecutive days. Now, you would like to find out the average noontime outdoor temperature in this place in the ten-day interval. What type of average do you have to use?
Arithmetic mean
Geometric mean
Harmonic mean
Weighted geometric mean

1003029506

Level: 
A
Let us assume that the value of an unique artwork will increase \( 1{.}5 \) times in the first year, \( 1{.}2 \) times in the second year and \( 1{.}9 \) times in the third year. We are interested in the compound annual growth rate in these three years. What type of average do we need to use?
Geometric mean
Arithmetic mean
Harmonic mean
Weighted arithmetic mean

1003029505

Level: 
A
Your stock portfolio had the following returns in the five consecutive years: \( 10\% \), \( -20\% \), \( 0\% \), \( 10\% \), \( 20\% \) (the minus sign denotes the financial loss). We are interested in five years compound annual growth rate of the portfolio. What type of average do we need to use?
Geometric mean
Arithmetic mean
Harmonic mean
Weighted arithmetic mean

1003029504

Level: 
A
In five consecutive years the annual production growth was \( 1\% \), \( 8\% \), \( 0\% \), \( 4\% \) and \( 1\% \) respectively. Find the compound annual growth rate of this five-year period. Round the result to two decimal places.
\( 2{.}76\% \)
\( 2{.}75\% \)
\( 2{.}72\% \)
\( 2{.}80\% \)

1003029503

Level: 
A
Paul drove the first halfway of a test track at a constant speed of \( 20\,\mathrm{kph} \) and the second halfway at a constant speed of \( 30\,\mathrm{kph} \). We wish to know Paul's average speed. What type of the average do we need to use?
Harmonic mean
Arithmetic mean
Geometric mean
Weighted arithmetic mean

1003029502

Level: 
A
Two employees work in a factory workroom. The first one completed an assigned task in \( 20 \) minutes, the second one completed the same task in \( 10 \) minutes. We are interested in the average time of the task completion. What type of the average do we need to use?
Arithmetic mean
Harmonic mean
Geometric mean
Weighted arithmetic mean