Statistics

1003025102

Level: 
A
A car travels the first quarter of its journey at an average speed of \( 50\, \mathrm{kph} \), the second quarter at an average speed of \( 90\, \mathrm{kph} \), the third quarter at an average speed of \( 130\, \mathrm{kph} \) and the remaining one quarter at an average speed of \( 80\, \mathrm{kph} \). What is the average speed of the car during the journey? Round the result to two decimal places.
\( 77{.}97\, \mathrm{km}/\mathrm{h} \)
\( 85{.}00\, \mathrm{km}/\mathrm{h} \)
\( 87{.}50\, \mathrm{km}/\mathrm{h} \)
\( 82{.}71\, \mathrm{km}/\mathrm{h} \)

1003025103

Level: 
A
Ten workers produce the same type of components. Two workers produce one component in \( 4 \) minutes, other three workers in \( 5 \) minutes, another one worker in \( 6 \) minutes, next three workers in \( 7 \) minutes and the last one of them in \( 8 \) minutes. What is the average time needed to produce one component? Round the result to the nearest hundredth.
\( 5{.}49\,\mathrm{min} \)
\( 5{.}50\, \mathrm{min} \)
\( 5{.}65\, \mathrm{min} \)
\( 5{.}80\, \mathrm{min} \)

1003025104

Level: 
A
The annual production of a business is recorded in the following table. Find the compound annual growth rate over the time period \( 2014 \) - \( 2017 \). (I.e., the average annual coefficient of the production growth, i.e., the ratio that provides a constant growth rate over the time period.) Round the result to four decimal places.\[ \begin{array}{|c|c|c|c|c|} \hline \text{Year} & 2014 & 2015 & 2016 & 2017 \\\hline \text{Production (pcs)} & 20\: 000 & 20\: 400& 21\: 420 & 24\: 633 \\\hline \end{array}\]
\( 1{.}0719 \)
\( 1{.}0705 \)
\( 1{.}0733 \)
\( 1{.}0727 \)

1003029501

Level: 
A
In a toy-factory four workers make the same toys manually. In one \( 8 \) hour shift the first worker produced \( 12 \) toys, the second \( 10 \) toys, the third \( 16 \) toys and the fourth \( 12 \) toys. What was the average time to produce a toy on that work shift?
\( 38\,\mathrm{min}\ 24\,\mathrm{s} \)
\( 38\,\mathrm{min}\ 40\,\mathrm{s} \)
\( 39\,\mathrm{min}\ 30\,\mathrm{s} \)
\( 38\,\mathrm{min}\ 58\,\mathrm{s} \)

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

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

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.
\( 2{.}76\% \)
\( 2{.}75\% \)
\( 2{.}72\% \)
\( 2{.}80\% \)

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

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

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