Question

a bakery sells 11 types of sandwiches. here are their calorie amounts 283, 597, 598, 600, 604, 606, 607, 615, 616, 616, 617 identify all values that are outliers. if there is more than one outlier, separate them with commas if there are no outliers, click on
one\.

Explanation:

Step1: Sort the data

First, sort the data set \(283,597,598,600,604,606,607,615,616,616,617\) in ascending order: \(283,597,598,600,604,606,607,615,616,616,617\).

Step2: Calculate the quartiles

The number of data points \(n = 11\).
The first - quartile \(Q_1\):
Since \(n = 11\), the position of \(Q_1\) is \(\frac{n + 1}{4}=\frac{11+1}{4}=3\). So \(Q_1 = 598\).
The third - quartile \(Q_3\):
The position of \(Q_3\) is \(\frac{3(n + 1)}{4}=\frac{3\times(11 + 1)}{4}=9\). So \(Q_3=616\).
The inter - quartile range \(IQR=Q_3 - Q_1=616 - 598 = 18\).
The lower fence \(=Q_1-1.5\times IQR=598-1.5\times18=598 - 27=571\).
The upper fence \(=Q_3 + 1.5\times IQR=616+1.5\times18=616 + 27=643\).

Step3: Identify the outliers

A value is an outlier if it is less than the lower fence or greater than the upper fence.
Since \(283<571\), the value \(283\) is an outlier.

Answer:

\(283\)