1. The standard deviation, like the range and the IQR, is a measure of dispersion, that is a measure of how spread out the data is. The larger the standard deviation, the more spread out the data is.
Whereas the IQR measures the spread either way from the median, the standard deviation measures the spread either way from the mean.
A formula to compute the standard deviation is as follows:
s = [(S (Xi - m)2 ) / N ]1/2
where the Xi s are data, m is the mean, and N is the number of data points. Note s 2 is called the variance.
Use this formula to compute the standard deviations for Fluffy's and Patches' kitten litter sizes. Round your means to the nearest whole number before using the formula (for just this problem).
a. Fluffy's kitten litter sizes: 2, 6, 5, 8, 9, 5, 3, 6
b. Patches' kitten
litter sizes: 1, 2, 4, 2, 3, 2, 3, 1
2. z-scores are used to compare students' performances or to compare the performance of one student with that of an entire class.
A z-score of zero means that the student's score was at the class mean. Positive z-scores are scores above the class mean, and negative z-scores are scores below the class mean.
A formula to compute z-scores
is Z = (X - m) / s
where X is a student's
raw score, m is the class mean, and s is the standard deviation.
a. If Marcy's MTH 554 score on Test 1 is 86, and if the class mean is 88 with a standard deviation of 4, what is her z-score?
b. Jack got a 99 on the same test. What is his z-score?
c. Stacy got a score
of 91. What is her z-score?