Statistics

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.

9000153306

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

9000153308

Level: 
B
Statistical file contains repeating measurements of a body mass in kilograms. Find the change in the coefficient of variation if we convert all data in the file to grams.
The coefficient of variation does not change.
The coefficient of variation becomes bigger.
The coefficient of variation becomes smaller.

9000153310

Level: 
B
Student did repeated measurements of the coefficient of friction, which is a dimensionless quantity. The mean of the measurements is \(0.6\) and the coefficient of variation (relative error) \(10\%\). From statistics it is known that with a probability nearly \(100\%\) the value of the coefficient is in the interval centered at the mean and having radius equal to the triple of the standard deviation. Find the upper bound of this interval.
\(0.78\)
\(0.18\)
\(0.42\)
\(0.66\)

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. \[ \begin{array}{|c|c|c|c|c|c|} \hline x & 5 & 6 & 7 & 9 & 11 \\\hline y & 3 & 2 &4 & 6 & 8 \\\hline \end{array} \]
\( 0{.}9569 \)
\( 0{.}9659 \)
\( 0{.}9695 \)
\( 0{.}9596 \)

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: \( r = 0{.}9289 \)

2010018105

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. \[ \begin{array}{|c|c|c|c|c|c|} \hline x & 1 & 2 & 3 & 4& 4.5 \\\hline y & 6 & 4 &5 & 3 & 3.5 \\\hline \end{array} \]
\(-0.8120\)
\(-0.8211\)
\(-0.8305\)
\(-0.8021\)