Problem 1:
Consider the following set of sample data:
78 121 143 88 110 107 62 122 130 95 78 139 89 125
a. Compute the mean and standard deviation for these sample data.
b. Calculate the coefficient of variation for these sample data and interpret its meaning
c. Using Tchebysheff's Theorem, determine the range of values that should include at least 89% of the data. Count the number of data values that fall into this range and comment on whether your interval range was conservative or not.
Problem 2:
Consider the following population:
71 89 65 97 46 52 99 41 62 88
73 50 91 71 52 86 92 60 70 91
73 98 56 80 70 63 55 61 40 95
a. Determine the mean and variance.
b. Determine the percentage of data values that fall in each of the following intervals:
c. Compare these with the percentages specified by Tchebysheff theorem.