In an experiment to assess the effect of listening to audiobooks while driving, participants are asked to
drive down a straight road in a driving simulator. The accompanying data on time (in milliseconds) to react
when a pedestrian walks into the street for 10 drivers listening to an audiobook are consistent with
summary statistics and graphs that appear in a paper
1,013 1,006 1,053 985 930 1,021 1,068 1,010 861 1,105
Calculate the variance (in milliseconds ) and standard deviation (in milliseconds) for this data set. (Round
your answers to four decimal places.)
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To calculate the variance and standard deviation, first find the mean of the data set.
Mean (μ) = (1,013 + 1,006 + 1,053 + 985 + 930 + 1,021 + 1,068 + 1,010 + 861 + 1,105) / 10 = 9,962 / 10 = 996.2
Next, subtract the mean from each data value and square the result.
(1,013 - 996.2)^2 = 249.64
(1,006 - 996.2)^2 = 95.84
(1,053 - 996.2)^2 = 3,212.04
(985 - 996.2)^2 = 124.84
(930 - 996.2)^2 = 4,338.04
(1,021 - 996.2)^2 = 612.04
(1,068 - 996.2)^2 = 5,197.64
(1,010 - 996.2)^2 = 189.44
(861 - 996.2)^2 = 18,047.24
(1,105 - 996.2)^2 = 11,810.24
Now, find the sum of all the squared differences:
249.64 + 95.84 + 3,212.04 + 124.84 + 4,338.04 + 612.04 + 5,197.64 + 189.44 + 18,047.24 + 11,810.24 = 43,877.52
Divide this sum by the number of data points (10) to find the variance:
Variance (σ^2) = 43,877.52 / 10 = 4,387.752
Finally, take the square root of the variance to find the standard deviation:
Standard Deviation (σ) = √4,387.752 = 66.2412
Rounded to four decimal places, the variance is 4,387.752 milliseconds and the standard deviation is 66.2412 milliseconds.