Answer :
The average (X) of the given sample data is approximately 89.48.
To find the average (X) of the sample data, we sum up all the values and divide it by the total number of values. In this case, we have 10 values in the sample. Let's calculate the average:
Average (X) = (76.3 + 84 + 81.5 + 95.8 + 98.5 + 92.5 + 94 + 87.4 + 94.6 + 86.7) / 10
After performing the calculation, we get X ≈ 89.48.
Now, let's move on to calculating the standard deviation (s) of the sample. The standard deviation measures the dispersion or spread of the data points around the average.
The formula for sample standard deviation (s) is given by:
s = √[(Σ(xi - X)^2) / (n - 1)]
Where Σ represents the sum of values, xi is each value in the sample, X is the average, and n is the number of values in the sample.
Using the given data, we substitute the values into the formula:
s = √[((76.3 - 89.48)^2 + (84 - 89.48)^2 + (81.5 - 89.48)^2 + (95.8 - 89.48)^2 + (98.5 - 89.48)^2 + (92.5 - 89.48)^2 + (94 - 89.48)^2 + (87.4 - 89.48)^2 + (94.6 - 89.48)^2 + (86.7 - 89.48)^2) / (10 - 1)]
After performing the calculations, we find that the sample standard deviation (s) is approximately 6.5.
Learn more about average:
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