Given the sample data.
x:22 14 14 16 29
(a) Find the range.
(b) Verify that Σx = 95 and Σx2 = 1973.
Σx
Σx2
(c) Use the results of part (b) and appropriate computation formulas to compute the sample variance s2 and sample standard deviation s. (Enter your answers to one decimal place.)
s2
s
(d) Use the defining formulas to compute the sample variance s2 and sample standard deviation s. (Enter your answers to one decimal place.)
s2
s
(e) Suppose the given data comprise the entire population of all x values. Compute the population variance σ2 and population standard deviation σ. (Enter your answers to one decimal place.)
σ2
σ
+33615 a) The range is simply the difference between the largest and the smallest.
b) I'm sure you can add them up to find Σx and add up the squares to find Σx2 by yourself!
c) The sample variance is \(s^2=\frac{\sum{(x-\mu)^2}}{n-1}\quad\text{ where }\mu\text{ is the mean and n is the number of terms}\\s \text{ is simply the square root of }s^2\)
d) The population variance is similar to the sample variance except that the divisor is just n instead of n-1.
.
+33615 a) The range is simply the difference between the largest and the smallest.
b) I'm sure you can add them up to find Σx and add up the squares to find Σx2 by yourself!
c) The sample variance is \(s^2=\frac{\sum{(x-\mu)^2}}{n-1}\quad\text{ where }\mu\text{ is the mean and n is the number of terms}\\s \text{ is simply the square root of }s^2\)
d) The population variance is similar to the sample variance except that the divisor is just n instead of n-1.
.
