Final answer:
To find the standard deviation of the given data set, calculate the mean, subtract the mean from each value, and square the result. Sum up all the squared differences, divide by the total number of values minus 1, and take the square root to get the standard deviation. The standard deviation of the data set is approximately 7.94.
Step-by-step explanation:
To find the standard deviation of the data set, we first need to calculate the mean of the data. The mean is found by adding up all the values and dividing by the total number of values. In this case, the mean is (98 + 95 + 82 + 85 + 77 + 85 + 91 + 93 + 75 + 80 + 81 + 90) / 12 = 87.0833.
Next, we subtract the mean from each value and then square the result. For example, (98 - 87.0833)² = 119.4697.
We repeat this process for all the values, then sum up all the squared differences. Divide the sum by the total number of values minus 1 (in this case, 12 - 1 = 11) to get the variance. Finally, take the square root of the variance to obtain the standard deviation. The standard deviation of this data set is approximately 7.94.
The standard deviation shows us how spread out the data is from the mean. In this case, the scores vary on average by about 7.94 points from the mean score of 87.0833.