Answer :
The mean of the given data is approximately 30.54, the variance is approximately 249.88, and the standard deviation is approximately 15.81.
To calculate the mean, standard deviation, and variance for the given data, we can use technology such as a calculator or a spreadsheet program.
Mean (average):
To find the mean, we add up all the numbers in the data set and then divide the sum by the total number of values. In this case, we have 7 values.
Mean = (39.3 + 38.2 + 11.7 + 40.1 + 23.5 + 42.6 + 15) / 7
= 30.543 rounded to two decimal places.
Variance:
The variance measures how spread out the data is from the mean. We calculate the variance by taking each data point, subtracting the mean, squaring the result, and then taking the average of those squared differences.
Variance =[tex][(39.3 - 30.543)^2 + (38.2 - 30.543)^2 + (11.7 - 30.543)^2 + (40.1 - 30.543)^2 + (23.5 - 30.543)^2 + (42.6 - 30.543)^2 + (15 - 30.543)^2] / 7[/tex]
= 249.877 rounded to two decimal places.
Standard Deviation:
The standard deviation is the square root of the variance and represents the average amount by which each data point deviates from the mean.
Standard Deviation = √Variance
= √249.877
= 15.810 rounded to two decimal places.
The mean of the given data is approximately 30.54, the variance is approximately 249.88, and the standard deviation is approximately 15.81.
To know more about Standard Deviation visit:
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