The 100–meter backstroke swimming times of the 8 swimmers during the semifinal and the finals of the Olympic games gives;
First part;
The center of the semifinal round is approximately 57.3625
The variability in the semifinal round is 0.0998
Second part;
The center of the final round is approximately 57.0125
The variability in the final round is 0.3336
How can the center and variability of the data in the dot plot be found?
The times of the swimmers in the semifinal round are;
56.7, 57.2, 57.3, 57.3, 57.4, 57.5, 57.7, 57.8
The central value is given by the mean of the data, is found as follows;
(56.7+57.2+57.3+57.3+57.4+57.5+57.7+57.8)/8 = 57.3625
The variability is given by the standard deviation which is found by the formula;
[tex] \sigma = \sqrt{ \frac{ x_{i} - \mu}{n} } [/tex]
Where;
[tex]x _{i} = the \: ith \: value[/tex]
[tex] \mu = the \: mean[/tex]
The standard deviation found using the given values above and an online tool is presented as follows;
[tex] \sigma = \sqrt{ \frac{ x_{i} - 57.3625}{8} \approx 0.316 } [/tex]
- The variance ≈ √(0.316) ≈ 0.0998
Second part;
In the final, we have the following values from the dot plot;
56, 56.6, 56.6, 57, 57.1, 57.2, 57.7, 57.9
From the above values, using an online calculator, the center, which is taken as the mean is 57.0125
The variance for the final, [tex] \sigma^2 [/tex] ≈ 0.3336
Learn more about finding the variance of a set of data here:
https://brainly.com/question/25639778
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