twenty high school students took an examination and received the following scores: 70, 60, 75, 68, 85, 86, 78, 72, 82, 88, 88, 73, 74, 79, 86, 82, 90, 92, 93, 73 determine what percent of the students scored within ( ) one standard deviation of the mean

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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