Answer:
Approximately 20.33 (rounded to two decimal places)
Explanation:
To find the standard deviation, we will first find the mean (average) of the scores, then find the variance, and finally take the square root of the variance to get the standard deviation.
Calculate the mean:
(80 + 30 + 34 + 32 + 55 + 27 + 38 + 41 + 84) / 9 = 421 / 9 = 46.78 (rounded to two decimal places)
Calculate the variance:
a. Find the difference between each score and the mean, and then square the differences (rounded to two decimal places).
(80 - 46.78)^2 = 1103.57
(30 - 46.78)^2 = 281.57
(34 - 46.78)^2 = 163.33
(32 - 46.78)^2 = 218.45
(55 - 46.78)^2 = 67.57
(27 - 46.78)^2 = 391.25
(38 - 46.78)^2 = 77.09
(41 - 46.78)^2 = 33.41
(84 - 46.78)^2 = 1385.33
b. Find the sum of the squared differences.
1103.57 + 281.57 + 163.33 + 218.45 + 67.57 + 391.25 + 77.09 + 33.41 + 1385.33 = 3721.57
c. Divide the sum of the squared differences by the number of scores (n = 9).
3721.57 / 9 = 413.51 (rounded to two decimal places)
Calculate the standard deviation:
Take the square root of the variance.
√413.51 = 20.33 (rounded to two decimal places)
The standard deviation of the scores is approximately 20.33 (rounded to two decimal places).