Answer :
Final answer:
The standard deviation of the provided scores is approximately 14.22. This number represents the average amount by which each individual score deviates from the mean score. The calculation involves few steps which include finding the mean of the data, subtracting the mean from each score, squaring those results, finding the average of those squared results, and taking the square root of that average.
Explanation:
The standard deviation is a measure of the amount of variability or dispersion in a set of values and tends to give a clear picture on how spread out the numbers are.
The first step is to find the mean (average) of the data set. Add up all the numbers and then divide by the number of values. In the given data set, adding up all the numbers gives 2053 and since there are 31 values, the mean would be 2053/31 = 66.22580645161290.
Next, subtract the mean from each number and square the result. For example, the first value is 0 - 66.22580645161290 = -66.22580645161290, and (-66.22580645161290)² = 4381.87 (rounded to two decimal places).
Do this for each number and add all these squared results together. After you do this, the sum of all these squared results is approx 6270.64516129034.
The next step is to find the average of these squared differences. This is done by dividing the sum of the squared differences by the total number of values, which gives (6270.64516129034) / 31 = 202.28 .
Finally, to get the standard deviation, take the square root of the average of these squared differences. The standard deviation of the fall 2020 midterm grades mentioned in your data set is, therefore, the square root of 202.28, which is approximately 14.22.
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