Statistics

1003134409

Level: 
C
Twenty-five students of the \( 7 \)th grade took an IQ test and SAT Reasoning Test. Results of the tests are denoted by IQ and SQ in headers of the following cross table. In the table the numbers of students are listed according to the results in both tests, while the results of both tests are classified in intervals. Determine the correlation coefficient between IQ and SQ. Round the result to four decimal places. Use your calculator in Statistics mode to carry out statistical calculations. \[ \begin{array}{|c|c|c|c|c|} \hline \textbf{SQ \ IQ} & \mathbf{(85;95]} & \mathbf{(95;105]} & \mathbf{(105;115]} & \mathbf{(115;125]} \\\hline \mathbf{(40;60]} & 1 & & & \\\hline \mathbf{(60;80]} & & 10 & 6 & 1 \\\hline \mathbf{(80;100]} & & & 6 & 1 \\\hline \end{array}\]
\( 0{.}6086 \)
\( 0{.}0086 \)
\( 0{.}9605 \)
\( -0{.}6806 \)

1103134408

Level: 
C
The values of variables \( x \) and \( y \) are listed in the following table and visualized in the next graph. Calculate the correlation coefficient of \( x \) and \( y \) and round it to four decimal places. \[ \begin{array}{|c|c|c|c|c|c|} \hline x & 5 & 6 & 7 & 9 & 11 \\\hline y & 3 & 2 &4 & 6 & 8 \\\hline \end{array} \]
\( 0{.}9569 \)
\( 0{.}9659 \)
\( 0{.}9695 \)
\( 0{.}9596 \)

1003134407

Level: 
B
In the tables below the absent hours in lessons of \( 16 \) boys and \( 14 \) girls from one class for half of a year are listed. Use the variance of the number of absent hours to find out the students of which gender had the absence more balanced. I.e. choose the group with more balanced absence and the correct variance of the number of absent hours. The variance is rounded to two decimal places. \[ \begin{array}{|c|c|c|c|c|c|c|c|} \hline \text{Girl's ID} & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\\hline \text{Absent hours} & 27 & 61 & 38 & 61 & 17 & 39 & 61 \\\hline \\\hline \text{Girl's ID} & 8 & 9 & 10 & 11 & 12 & 13 & 14 \\\hline \text{Absent hours} & 25 & 21 & 52 & 16 & 34 & 9 & 25 \\\hline \end{array} \] \[ \begin{array}{|c|c|c|c|c|c|c|c|c|c|c|} \hline \text{Boy's ID} & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \\\hline \text{Absent hours} & 67 & 56 & 26 & 36 & 27 & 55 & 17 & 34 \\\hline \\\hline \text{Boy's ID} & 9 & 10 & 11 & 12 & 13 & 14 & 15 & 16 \\\hline \text{Absent hours} & 54 & 46 & 13 & 48 & 21 & 49 & 18 & 14 \\\hline \end{array} \]
boys: \( \sigma^2= 285{.}34\,\mathrm{lessons}^2 \)
girls: \( \sigma^2= 297{.}35\,\mathrm{lessons}^2 \)
boys: \( \sigma^2= 16{.}89\,\mathrm{lessons} \)
girls: \( \sigma^2= 17{.}24\,\mathrm{lessons} \)

1103134405

Level: 
B
The students are evaluated according to the grading scale from \( 1 \) to \( 5 \), while \( 1 \) is the best grade and \( 5 \) is the worst one. In the pictures, there are visualizations of relative frequencies of grades in Math, which students of two groups (A and B) had in their year-class-reports. Calculate the variance of grades for each group of students and determine, in which group student performances of Math knowledge are more balanced. I.e. from the offered choices choose the group, which has more balanced grades and with the correct variance of grades. The variance is rounded to two decimal places.
A: \( 0{.}81 \)
B: \( 0{.}84 \)
A: \( 0{.}90 \)
B: \( 0{.}92 \)

1003134403

Level: 
B
The average age of town citizens decreased by \( 19\,\% \) due to a satellite town construction. The variance of the age has increased by \( 21\,\% \). Complete the correct statement. The coefficient of variation .... (Note: The results are rounded to two decimal places.)
increased by \( 35{.}80\,\% \).
increased by \( 49{.}38\,\% \).
decreased by \( 33{.}06\,\% \).
decreased by \( 26{.}36\,\% \).

1003134402

Level: 
B
There are two groups, A and B, of students in German language class. Each group consists of \( 15 \) students. In the tables, down each column, a student’s ID and grade from the mid-year’s grade report are listed. The students are evaluated according to the grading scale from \( 1 \) to \( 5 \), while \( 1 \) is the best grade and \( 5 \) is the worst one. Calculate the coefficient of variation of grades for each group and determine in which group the grades are more balanced. I.e. choose the name of the group with more balanced grades and with the correct coefficient of variation (\( \% \)) of grades. The value of the coefficient of variation is rounded to two decimal places. \[ \begin{array}{|c|c|c|c|c|c|c|c|c|}\hline \textbf{A -- students} & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \\\hline \textbf{Grade} & 2 & 2 & 2 & 2 & 3 & 2 & 1 & 2 \\\hline \\\hline \textbf{A -- students} & 9 & 10 & 11 & 12 & 13 & 14 & 15 & \\\hline \textbf{Grade} & 2 & 1 & 3 & 1 &3 & 2 & 3 & \\\hline \end{array} \] \[ \begin{array}{|c|c|c|c|c|c|c|c|c|}\hline \textbf{B -- students} & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \\\hline \textbf{Grade} & 2 & 1 & 1 & 2 & 2 & 3 & 1 & 2 \\\hline \\\hline \textbf{B -- students} & 9 & 10 & 11 & 12 & 13 & 14 & 15 & \\\hline \textbf{Grade} & 2 & 1 & 2 &1 &1 &1 &1 & \\\hline \end{array} \]
A: \( 32{.}90\,\% \)
A: \( 3{.}04\,\% \)
B: \( 40{.}32\,\% \)
B: \( 2{.}48\,\% \)

1003134401

Level: 
B
We want to compare the performances of two javelin throwers in one competition. Throws of Alex and Martin (in meters) are recorded in the following table. Calculate the coefficient of variation for each set of results and determine, which of the athletes has more balanced performance. I.e. choose the name of the athlete with more balanced performance and with the correct coefficient of variation (\( \% \)) of his throws. The coefficient of variation is rounded to two decimal places. \[ \begin{array}{|c|c|c|c|c|} \hline \textbf{Alex} & 78.95 & 83.32 & 86.14 & 84.46 \\\hline \textbf{Martin} & 84.66 & 83.63 & 76.83 & 83.23 \\\hline \end{array} \]
Alex: \( 3{.}20\,\% \)
Alex: \( 27{.}99\,\% \)
Martin: \( 4{.}52\,\% \)
Martin: \( 23{.}52\,\% \)

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