Basic Statistics 2011

Module 2

Summation Notation and Use of the Calculator

Objectives:

At the end of the module, the students should be able to:

1. Determine the values of expressions using the summation notation2. Utilize the calculator in evaluating expressions involving the summation notation

The most common symbol in Statistics is the Greek letter sigma, ∑, which is used to denote summation.

∑i=1

n

x i isread as the summation of {x} rsub {i} as i goes from 1 to n

where i is the lower limit and n the upper limit. In some cases, the subscript i can be omitted.Examples: Let x1=6, x2=9, x3=10, x4=8, and x5=5.

Find: a)

b) ∑ x

c) ∑ x2

d)(∑ x )2

e)∑ (x+1)Solution:

a. Since lower and upper limits are stated, ∑i=1

3

x i=x1+x2+ x3=6+9+10=25

For b to e, no limits are specified, hence all values should be considered.

b. ∑ x=6+9+10+8+5=38

c. ∑ x2=62+92+102+82+52=306

d. (∑ x )2=(6+9+10+8+5)2=1444

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e. ∑ (x+1 )= (6+1 )+(9+1 )+(10+1 )+ (8+1 )+(5+1 )=43

How to Use your Scientific Calculator*

*Caution: The procedure may not apply to all calculator models, thus, you may just consult your calculator’s manual.

For data involving one variable, activate the STAT 0 or STAT 1 mode or its equivalent.

1. Set your calculator in SD mode. Press Mode and choose STAT then SD.

2. Clear the Stat memory by pressing 2nd F or Shift then CLR, or AC, or CA.

3. Start entering data. Using the data in the example above

X1 X2 X3 X4 X56 9 10 8 5

Press 6 DATA9 DATA10 DATA8 DATA5 DATA4. To get ∑ x , press RCL then the key where ∑ x is. It should display the same answer given above.

The same applies to getting ∑ x2.

5. You can also get other measurements like the mean (x ¿ and standard deviation (sx) by pressing RCL then the key where xor sx is, respectively.

For data involving two variables, activate the STAT 1 or STAT LINE mode or its equivalent.

1. Press MODE then STAT then LINE.2. Clear the Stat memory.3. Start entering data. Use the data below.

X 3 5 4 8 9y 12 15 16 11 13

Press 3 (x,y) 125 (x,y) 154 (x,y) 168 (x,y) 119 (x,y) 13

4. Press RCL then the key where the data you intend to get is placed.

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RCL ∑ x Did you get 29?

RCL ∑ y 67?

RCL ∑ x2 What did you get?

How about…

1. ∑ y2

2. ∑ xy

3. x

4. y

5. sy

6. sx

Exercise:

A. The following are the number of minutes it took 10 students to answer a 10-item quiz in Algebra.

Student Number 1 2 3 4 5 6 7 8 9 10Number of Minutes (m) 10 5 15 20 8 19 25 30 17 11

Find:

1. ∑ m

2. ∑ m2

3. (∑ m)2

4. m5. sm

B. The following table shows the 2nd quarter grades of 10 students in English and Geometry.

English (x) 91 88 78 85 83 90 89 86 89 88Geometry(y) 87 86 80 89 85 86 89 87 85 83

Find:

1. ∑ x

2. ∑ x2

3. ∑ y

4. ∑ y2

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5. ∑ xy

6. ¿7. (∑ x )2

8. (∑ y )2

9. ∑i=2

8

x i

10. ∑i=3

9

yi

11. x12. y13. x σn−1∨sx14. x σn∨σx15. r

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