Multiple choice

The exam scores of 9 students in a class are represented by the set S = {68, 62, 78, 73, 82, 88, 76, 71, 77}. Which of the following options accurately represents the value of the standard deviation for this set of scores?

  1. 2.37

  2. 3.72

  3. 5.78

  4. 7.23

  5. 8.25
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Mean = (68+62+78+73+82+88+76+71+77)/9 = 675/9 = 75. Variance = [(68-75)^2 + (62-75)^2 + (78-75)^2 + (73-75)^2 + (82-75)^2 + (88-75)^2 + (76-75)^2 + (71-75)^2 + (77-75)^2]/9 = (49+169+9+4+49+169+1+16+4)/9 = 470/9 = 52.22. Standard deviation = sqrt(52.22) = 7.226.

AI explanation

The formula for standard deviation requires finding the mean, which is the sum of the scores divided by 9, yielding 75.5. Next, you find the squared difference of each score from this mean, sum those squared differences to get 471, and divide by 9 to get a variance of approximately 52.33. Taking the square root of 52.33 gives a standard deviation of approximately 7.23.

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