Statistics

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?
\( 38\,\mathrm{min}\ 24\,\mathrm{s} \)
\( 38\,\mathrm{min}\ 40\,\mathrm{s} \)
\( 39\,\mathrm{min}\ 30\,\mathrm{s} \)
\( 38\,\mathrm{min}\ 58\,\mathrm{s} \)

1003025201

Level: 
B
Two hunters, Adam and Boris, competed in target shooting. Adam hit the target points \( \{10;10;9;8;7\}\), and Boris \( \{10;10;9;9;6\} \). Who is the winner? In the case of the same sum of gained points the shooting accuracy is decisive. Which of the following statements is true, if the accuracy is quantified by the variance of the points? (The variance is rounded to two decimal places.)
Adam won with the variance of \( 1{.}36\,\mathrm{points}^2 \).
Adam won with the variance of \( 1{.}17\,\mathrm{points}^2 \).
Boris won with the variance of \( 2{.}16\,\mathrm{points}^2 \).
Adam won with the variance of \( 1{.}36\,\mathrm{points} \).
Adam won with the variance of \( 1{.}17\,\mathrm{points} \).
Boris won with the variance of \( 2{.}16\,\mathrm{points} \).

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.\[ \begin{array}{|c|c|c|c|c|} \hline \text{Year} & 2014 & 2015 & 2016 & 2017 \\\hline \text{Production (pcs)} & 20\: 000 & 20\: 400& 21\: 420 & 24\: 633 \\\hline \end{array}\]
\( 1{.}0719 \)
\( 1{.}0705 \)
\( 1{.}0733 \)
\( 1{.}0727 \)

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.
\( 5{.}49\,\mathrm{min} \)
\( 5{.}50\, \mathrm{min} \)
\( 5{.}65\, \mathrm{min} \)
\( 5{.}80\, \mathrm{min} \)

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.
\( 77{.}97\, \mathrm{km}/\mathrm{h} \)
\( 85{.}00\, \mathrm{km}/\mathrm{h} \)
\( 87{.}50\, \mathrm{km}/\mathrm{h} \)
\( 82{.}71\, \mathrm{km}/\mathrm{h} \)

1103025101

Level: 
A
The results of the math test are shown in the graph. Based on the graph, which of the following statements is false?
The median of the scores is the same as their modus.
Half of the students had higher score than the average score.
The average score rounded to the nearest hundredth is \( 2{.}68 \).

1003029402

Level: 
B
A sample of \( 50 \) pieces of pears was selected randomly from the production of the plant breeding institute. The weights of these pears are recorded in the table. \[ \begin{array}{|c|c|} \hline \text{ Weight (g) }&\text{ Number of pears } \\\hline 26\text{ -- }30&8 \\\hline31\text{ -- }35&14 \\\hline 36\text{ -- }40&15 \\\hline 41\text{ -- }45&9 \\\hline 46\text{ -- }50&4\\\hline\end{array}\] Calculate the variance of pear weights and round the variance to the nearest hundredth. (To solve the task with help of calculator is recommended.)
\( 33{.}81\,\mathrm{g}^2 \)
\( 5{.}81\,\mathrm{g}^2 \)
\( 15{.}84\,\mathrm{g}^2 \)
\( 39{.}84\,\mathrm{g}^2 \)

1003029401

Level: 
B
Wooden boards were expected to be cut to the same length. After their cutting the resulting measured lengths are: \( 2{.}00;\ 2{.}02;\ 2{.}05;\ 2{.}02;\ 2{.}08;\ 2{.}11 \) (in meters). We use the standard deviation of board lengths to describe (quantify) the accuracy of cutting. Find the standard deviation of board lengths rounded to four decimal places.
\( 0{.}0382\,\mathrm{m} \)
\( 0{.}0381\,\mathrm{m} \)
\( 0{.}0014\,\mathrm{m} \)
\( 0{.}0015\,\mathrm{m} \)

9000153304

Level: 
B
Two students performed repeated measurements of the same length. After evaluating statistical characteristics they got equal means of the length. Which of the following statement is true? (Remark: The accuracy is determined by the coefficient of variation.)
There is not enough information to compare the accuracy of both measurements.
One of the students measured with a better accuracy than the other.
Both students did their measurements with the same accuracy.

9000153305

Level: 
B
Two students performed repeated measurements of the same length. After evaluating statistical characteristics they got equal standard deviations. Which of the following statement is true? (Remark: The accuracy is determined by the coefficient of variation.)
There is not enough information to compare the accuracy of both measurements.
One of the students measured with a better accuracy than the other.
Both students did their measurements with the same accuracy.