Mrs. Jones Algebra 2 class scored very well on yesterday’s quiz. With one exception, everyone received an A. Within how many standard deviations from the mean do all the quiz grades fall? 91, 92, 94, 88, 96, 99, 91, 93, 94, 97, 95, 97
We know that the: mean = 93.9 standard deviation = 3.12
In calculating how many standard deviation a number is away from the mean, we simply deduct the mean from the highest and lowest number in the set, then dividing it by the standard deviation. This is also known as getting the z score which has the following formula:
Z = (highest/lowest number - mean)/ standard deviation
For the highest number which is 99, Z = (99 - 93.9) / 3.12 = 1.6 For the lowest number which is 88, Z = (88 - 93.9) / 3.12 = -1.89
All the quiz grades fall within 2 standard deviations away from the mean.
