summation notation

[comet2000]

In a study of the moon illusion that we will discuss in Chapter 5, Kaufman and Rock (1962) tested an earlier hypothesis by Holway and Boring (1940) about reasons for the moon illusion. Kaufman and Rock compared how subjects performed when they were able to first look at the moon with their eyes level, and then look again with their eyes elevated. The data for the Eyes Level condition follow: 1.65, 1.00, 2.03, 1.25, 1.05, 1.02, 1.67, 1.86, 1.56, 1.73

Using X to represent this variable,
(a) What are x3, x5, and x8?
x3 = 2.03, x5 = 1.05 and x8 =1.86
(b) Calculate ?x
?x = (1.65 + 1.00 + 2.03 + 1.25 + 1.05 + 1.02 + 1.67 + 1.86 + 1.56 + 1.73) = 14.82
(c) Write the summation notation for (b) in its most complex form.
i don't get this part.

 

[mmm4444bot]

… (c) Write the summation … in its most complex form …

Why makes things complex? :wink:

Seriously, I'm thinking that they want you to use Sigma notation to express the summation in its most concise form.

\(\displaystyle \sum_{n = 1}^{N} x_n\)

because it stands for

\(\displaystyle x_1 \;+\; x_2 \;+\; x_3 \;+\; x_4 \;+\; x_5 \;+\; \ldots \;+\; x_N\)

where N represents the total number of elements in your data set.

In other words, you need to count the number of elements in your data set x, and then replace N with this number when you write the Sigma notation.