Answer :
70% of students had scores that were within (±) one standard deviation of the mean.
Explain the term standard deviation?
- The term "standard deviation" (or "σ") refers to a measurement of the data's dispersion from the mean.
- A low standard deviation indicates that the data are grouped around the mean, whereas a high standard deviation shows that the data are more dispersed.
For the stated question-
Total number of students = 20
Scores received; 70, 60, 75, 68, 85, 86, 78, 72, 82, 88, 88, 73, 74, 79, 86, 82, 90, 92, 93, 73.
Mean = Sum of all/ Total number
Mean x = 79.7
standard deviation = 8.7
Thus, (±) one standard deviation SD of the mean becomes;
-1 SD; 79.7 - 8.7 ≈ 70.994
+1 SD; 79.7 + 8.7 ≈ 88.406
Thus, 71 to 88
Percentage = scores between 71 to 88/ total scores
Percentage = 14/20 x 100 %
Percentage = 70%
Thus, 70% of students had scores that were within (±) one standard deviation of the mean.
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