2
Mrs. Jones Algebra 2 class scored very well on yesterday's quiz. With one exception, everyone
received an A. Within how many standard deviations of the mean do all the quiz grades fall?
91, 92, 94, 88, 96, 99, 91, 93, 94, 97, 95, 97
(1 point)
C
O 1
O 4
To find the standard deviation, first calculate the mean of the quiz grades:
(91 + 92 + 94 + 88 + 96 + 99 + 91 + 93 + 94 + 97 + 95 + 97) / 12 = 93.25
Next, calculate the differences between each quiz grade and the mean:
-2.25, -1.25, 0.75, -5.25, 2.75, 5.75, -2.25, -0.25, 0.75, 3.75, 1.75, 3.75
To find the standard deviation, calculate the average of the squared differences:
((-2.25)^2 + (-1.25)^2 + 0.75^2 + (-5.25)^2 + 2.75^2 + 5.75^2 + (-2.25)^2 + (-0.25)^2 + 0.75^2 + 3.75^2 + 1.75^2 + 3.75^2) / 12
= (5.0625 + 1.5625 + 0.5625 + 27.5625 + 7.5625 + 33.0625 + 5.0625 + 0.0625 + 0.5625 + 14.0625 + 3.0625 + 14.0625) / 12
= 117.0625 / 12
≈ 9.755
Therefore, the standard deviation is approximately 9.755. Since all quiz grades are within one standard deviation of the mean (93.25), they all fall within one standard deviation.