Sigma Notation and Calculating the Arithmetic Mean · Exercise 10

A standardized test is given to ten people at the beginning of the school year with the results given in below. At the end of the year the same people were again tested.

(a) What is the average improvement?
(b) Does it matter if the means are subtracted, or if the individual values are subtracted?

$$\begin{array}{ccc}\text{Student}& \text{Beginning score}& \text{Ending score}\\ \text{1}& \text{1100}& \text{1120}\\ \text{2}& \text{980}& \text{1030}\\ \text{3}& \text{1200}& \text{1208}\\ \text{4}& \text{998}& \text{1000}\\ \text{5}& \text{893}& \text{948}\\ \text{6}& \text{1015}& \text{1030}\\ \text{7}& \text{1217}& \text{1224}\\ \text{8}& \text{1232}& \text{1245}\\ \text{9}& \text{967}& \text{988}\\ \text{10}& \text{988}& \text{997}\end{array}$$

OpenStax, Introductory Business Statistics 2e · §2.4 Sigma Notation and Calculating the Arithmetic Mean · Exercise 10