Create a problem for additional rules and do the two-way tables, please.

Explain the additional measure of central tendency would be appropriate to report with these data based on their findings.

Suppose we have data set: $19,21,22,22,28,31,33,44,50$. Find the interquartile range of this set.
First solution: Firstly, we should find the $75$th percentile of this set. $0,75\cdot 9=6,75$ and rounding up this number to nearest whole we get $7$. So the $75$th percentile of this set is $33$. Secondly, should find the $25$th percentile of this set. $0,25\cdot 9=2,25$ and rounding up this number to nearest whole we get $3$. So the $25$th percentile of this set is $22$. Hence,
$\text{interquartile range}=Q_3-Q_1=33-22=11.$
Second solution: The median of this set is $28$. First quartile is the median of lower set. Hence $Q_1={\displaystyle \frac{21+22}{2}}=21.5$, third quartile is the median of upper set. Hence $Q_3={\displaystyle \frac{33+44}{2}}=38.5$
$\text{interquartile range}=Q_3-Q_1=38.5-21.5=17.$
Which one is correct? Please explain why one of the solutions is false.

What is the number called that determines each unique T distribution?

A survey was designed to study how business operations vary according to their size. Companies were classified as small, medium, or large.

Refer to the Journal of Applied Psychology (Jan. 2011) study of the determinants of task performance. In addition to $x_1=$ conscientiousness score and $x_2=\{1\text{if highly complex job, 0 if not}\}$, the researchers also used $x_3=$ emotional stability score, $x_4=$ organizational citizenship behavior score, and $x_5=$ counterproductive work behavior score to model y = task performance score. One of their concerns is the level of multicollinearity in the data. A matrix of correlations for all possible pairs of independent variables follows. Based on this information, do you detect a moderate or high level of multicollinearity? If so, what are your recommendations?

$x_1{x}_2{x}_3{x}_4$

Conscientiousness $(x_1)$

Job Complexity $(x_2).13$

Emotional Stability $(x_3).62.14$

Organizational Citizenship $(x_4).24.03.24$

Counterproductive Work $(x_5)-.23-.23-.02-.62$

Sketch a scatterplot showing data for which the correlation is r = -1.

Construct 90% and 95% confidence intervals for the population proportion. Interpret the results and compare the widths of the confidence intervals. In a survey of 2149 U.S. adults in a recent year, 1241 made a New Year's resolution to eat healthier.