Question

summary: roger claims that the two statistics most likely to change greatly when an outlier is added to a small data set are the mean and the median. is rogers claim correct? 1) yes, both the mean and median are likely to change greatly. 2) no, only the mean is likely to change greatly. 3) no, only the median is likely to change greatly. 4) no, neither the mean nor the median are likely to change greatly. 5) there is not enough information to determine if the mean or the median is likely to change greatly. 1. given data set: -3, 5, 10, 12, 14, 18, 24, 26, 49, 60 which of the following statements is true regarding this data? choose: the value -3 is the only outlier. the value 60 is the only outlier. no outliers exist. multiple outliers exist.

Explanation:

Step1: Calculate quartiles

First, order the data set: -3, 5, 10, 12, 14, 18, 24, 26, 49, 60. There are \(n = 10\) data - points. The median (\(Q_2\)) is the average of the 5th and 6th ordered values. \(Q_2=\frac{14 + 18}{2}=16\). The lower half of the data is -3, 5, 10, 12, 14. The median of the lower half (\(Q_1\)) is 10. The upper half of the data is 18, 24, 26, 49, 60. The median of the upper half (\(Q_3\)) is 26.

Step2: Calculate the inter - quartile range (IQR)

\(IQR=Q_3 - Q_1=26 - 10 = 16\).

Step3: Determine the outlier boundaries

The lower outlier boundary is \(Q_1-1.5\times IQR=10-1.5\times16=10 - 24=-14\). The upper outlier boundary is \(Q_3 + 1.5\times IQR=26+1.5\times16=26 + 24 = 50\).

Step4: Identify outliers

The value -3 is within the range \(-14\) to 50, and the value 60 is greater than 50. So 60 is an outlier and there are no other outliers in the data set.

Answer:

The value 60 is the only outlier.