A set of measurements has given the following result for the measurement of x (in some u...

A set of measurements has given the following result for the measurement of x (in some units of length): 3.4, 3.9, 5.2, 4.7, 4.1, 3.8, 3.9, 4.7, 4.1, 4.5, 3.8, 4.5, 4.8, 3.9, and 4.4. Find the average value of x, called x or <x>, and average value of x², represented by <x ²>. Show that the standard deviation of x, given by

where x_i is the individual measurement and N is the number of measurements, is also give. Find the value of σ for the set of data given here.