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The reacttimes data set has 50 observations of human reaction times to a physical stimulus. The reaction times are named times and arranged in increasing order below. 0.12 0.30 0.35 0.37 0.44 0.57 0.61 0.62 0.71 0.80 0.88 1.02 1.08 1.12 1.13 1.17 1.21 1.23 1.35 1.41 1.42 1.42 1.46 1.50 1.52 1.54 1.60 1.61 1.68 1.72 1.86 1.90 1.91 2.07 2.09 2.16 2.17 2.20 2.29 2.32 2.39 2.47 2.60 2.86 3.43 3.43 3.77 3.97 4.54 4.73 1. Find the mean and median of times without using r. You may

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Solution: The formula for mean is:

[tex]Mean=\frac{\sum x}{n}[/tex]

Where:

[tex]\sum x[/tex] is the sum of given observations

[tex]n[/tex] is the number of observations

[tex]\sum x=87.12[/tex]

[tex]n=50[/tex]

[tex]\therefore Mean =\frac{87.12}{50}= 1.74[/tex] rounded to two decimal places

To find the median, we need to first arrange the data in ascending order but we are already given the data in ascending order.

Therefore, the median is:

[tex]Median=\left(\frac{n+1}{2} \right)^{th} item[/tex]

                  [tex]=\left(\frac{51}{2} \right)^{th} item[/tex]

                  [tex]=25.5^{th} item[/tex]

                  [tex]=1.52+0.5(1.54-1.52)[/tex]

                  [tex]=1.52+0.01[/tex]

                  [tex]=1.53[/tex]

Therefore, the median = 1.53

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