i is the index of the sum, it tells where to start the sum and where to end it.

INSTRUCTIONS TO CANDIDATES

ANSWER ALL QUESTIONS

Summation

Notation:

𝑛 ! 𝑎i = 𝑎$ + 𝑎2 + 𝑎& + ⋯ + 𝑎𝑛

i#$

∑ is a Greek letter sigma, this is an instruction to find the sum.

i is the index of the sum, it tells where to start the sum and where to end it.

Example:

𝑎1 = 1, 𝑎2 = 3, 𝑎3 = 5, 𝑎4 = 7, 𝑎5 = 9, 𝑎6 = 0, 𝑎7 = 2, 𝑎8 = 4, 𝑎9 = 6

 𝑖=1

 𝑥𝑖 is to add the terms 𝑥𝑖, starting with i = 1, and ending with i = 5.

! 𝑎𝑖 = 𝑎1 + 𝑎2 + 𝑎3 + 𝑎4 + 𝑎5 = 1 + 3 + 5 + 7 + 9 =

𝑖=1 4

! 𝑎𝑖 =

𝑖=3

Example: (Computer the following)

i#$

 𝑖 = 1 + 2 + 3 + 4 + 5 =

i#$

𝑖2 = 12 + 22 + 32 + 42 + 52 =

(i#$4𝑖 =

 In many statistics books, the index is often omitted.

∑ 𝑥 : sum of all x values.

Example: Given a data set:

3, 2, 5, 9, 11

a. Find ∑ 𝑥

! 𝑥 = 3 + 2 + 5 + 9 + 11 = 

b. Find ∑ 𝑥2

c. Find ∑ 𝑥/5 =

d. Find ∑(𝑥 − 6)2

Exercises:

Answer the following question using the given data

12 10 9 7 13 18 14 11 9 7

1. Find ∑ 𝑥

2. Find ∑ 𝑥2

3. Find (∑ 𝑥)2

4. Find ∑(𝑥 − 11)2

Attachments:

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