Statistics

1103134410

Level: 
C
The heights (\(\mathrm{cm}\)) of ten boys and their best performances (\(\mathrm{cm}\)) in standing long jump at the international athletic championship are listed in the following table. Determine the correlation coefficient \( r \) between height of boys and their longest jump. You can use a statistics mode of your calculator to carry out statistical computations. Round the result to four decimal places. Based on the following scatterplot and the correlation coefficient interpret the strength of linear relationship between analysed variables. \[ \begin{array}{|c|c|c|c|c|c|} \hline \textbf{Boy's height (cm)} & 189 & 175 & 187 & 183 & 174 \\\hline \textbf{Length of the jump (cm)} & 231 & 207 & 214 & 223 & 202 \\\hline \\\hline \textbf{Boy's height (cm)} & 193 & 179 & 169 & 186 & 183 \\\hline \textbf{Length of the jump (cm)} & 242 & 229 & 190 & 226 & 212 \\\hline \end{array} \]
strong linear relationship: \( r = 0{.}8628 \)
moderate linear relationship: \( r = 0{.}5542 \)
moderate linear relationship: \( r = 0{.}7444 \)
strong linear relationship: \( r = 0{.}9289 \)

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: \( 0{.}92 \)