Question

(b) find the interquartile range (iqr) of the data set.

(c) calculate a lower boundary using ( q _ { 1 } - 1.5 cdot mathrm { iqr } ). calculate an upper boundary using ( q _ { 3 } + 1.5 cdot mathrm { iqr } ). (note that ( 1.5 cdot mathrm { iqr } ) means 1.5 times the iqr.)

(d) any values less than the lower boundary or greater than the upper boundary are considered outliers. identify all the outliers of the data set. if there is more than one outlier, separate them with commas. if there are no outliers, click
one\.

Explanation:

Step1: Recall the formula for IQR

IQR = \(Q_3 - Q_1\). Given \(Q_1 = 77\) and \(Q_3=89\), then \(IQR=89 - 77=12\).

Step2: Calculate the lower and upper boundaries

Lower boundary formula: \(Q_1-1.5\times IQR\). Substitute \(Q_1 = 77\) and \(IQR = 12\), we get \(77-1.5\times12=77 - 18=59\).
Upper boundary formula: \(Q_3 + 1.5\times IQR\). Substitute \(Q_3 = 89\) and \(IQR = 12\), we get \(89+1.5\times12=89 + 18=107\).

Step3: Identify outliers

Since no data values are provided in the problem statement (assuming we just follow the calculation - based on the given boundaries from previous steps and no data to check against, but if we assume the problem is just about the calculation part for (d) as per the structure of the question - if we consider the general case of outlier identification which is values \(<59\) or \(>107\). But since no data set is given to check, if we assume the problem is just showing the process (as in a software - like interface where (a) - (c) are filled and (d) is to be filled based on the logic. But if we consider the calculation part for (d) in terms of formula application (even without data) - but if we assume that the user just wants the format followed as per the previous steps (as in a practice problem where (a) - (c) are given and (d) is to be answered as no data, but in the context of the problem's structure (like a stats software where (a) - (c) are input and (d) is output). But if we consider the formula - based outlier definition. However, since no data is provided to check against \(59\) and \(107\), if we assume that this is a follow - up of a data - set problem (where maybe in the original data - set (not shown here) there are no values \(<59\) or \(>107\)).

Answer:

None