Question

the 10 participants in an experiment had the following reaction times (in milliseconds).
495, 495, 497, 498, 502, 504, 505, 506, 507, 509
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: Find the median

First, find the median of the data set. Since there are \(n = 10\) data points (\(x_1=495,x_2 = 495,x_3=497,x_4=498,x_5=502,x_6=504,x_7=505,x_8=506,x_9=507,x_{10}=509\)), the median \(Q_2=\frac{x_5 + x_6}{2}=\frac{502+504}{2}=503\).

Step2: Find \(Q_1\) and \(Q_3\)

The lower half of the data is \(x_1,x_2,x_3,x_4,x_5\) (495, 495, 497, 498, 502). The median of the lower half \(Q_1 = 497\). The upper half of the data is \(x_6,x_7,x_8,x_9,x_{10}\) (504, 505, 506, 507, 509). The median of the upper half \(Q_3=506\).

Step3: Calculate the inter - quartile range (IQR)

\(IQR=Q_3 - Q_1=506 - 497 = 9\).

Step4: Determine the outlier boundaries

The lower boundary is \(Q_1-1.5\times IQR=497-1.5\times9=497 - 13.5 = 483.5\). The upper boundary is \(Q_3 + 1.5\times IQR=506+1.5\times9=506+13.5 = 519.5\).

Step5: Check for outliers

All data points \(495,495,497,498,502,504,505,506,507,509\) are within the range \([483.5,519.5]\).

Answer:

None