Sigma Notation is the Greek letter sigma, and is used to represent the sum of an

ordered list of variables. It is also referred to as Summation.

23

1

( 1)2k

k

2 2 2( ) ( )12 1 2 1 2 1( )2 3 2 2 21 3( ) 5( ) ( ) 1 9 25 35

5

3

(2)5 k

k

5

3

5 (2)k

k

3 4 5( ) ( ) (2)5 2 2 8 165 32( ) )5(56 280

Asi De Facil

Regents Questions

JUN05 23

DefCon 2

( ) ( )3co ( ) ( )s 1 3cos 1 3cos 1 3cos0 1 2 3 1 3 1 3cos 1 30 2cos 1 3cos( 3 1)

4 2 4 2 4

1 2 3 41 1 1 18 16

2 2 2 2

AUG04 18

DefCon 1

1 1 1 18 16

2 4 8 16

158 16

16

8 15 23 Asi De Facil

1 3 1 33 1 1( ) ( ) ( ) 111 3

Comparing Statistical Data

Mean Median Mode

The average of a set of scores or data.

The middle score or number when they are in ascending order.

The score or number that appears most often.

The Mean, Median, and Mode are measures of Central Tendency because they indicate where the data are centered.

Range Standard Deviation

The difference between the largest and the smallest score or number.

A statistic that measures how far apart the individual scores or numbers are from the mean.

The Range, and Standard Deviation are measures of Dispersion because they indicate how spread out the data are.

Calculating Standard Deviation

A) Calculate the standard deviation of set A = {49, 53, 51, 55}

Store the data in L1

Press STAT > (CALC) ENTER (1-Var Stats) ENTER

2

1-Var Stats

52

208

10836

2.581988897

2.236067977

4

X

x

x

Sx

x

n

B) Calculate the standard deviation of set B = {1, 2, 5, 200}

2nd L2 ENTER

2

1-Var Stats

52

208

40030

98.68130522

85.4605172

4

X

x

x

Sx

x

n

For set B the standard deviation is large compared to the mean which suggests that the individual numbers vary widely from the mean.

Grouping DataThe accompanying table represents the

test scores of 30 math students.

Grade Frequency

100 2

95 3

94 1

88 3

85 4

79 5

74 3

65 9

a) Find the mean score and the standard deviation, correct to the nearest tenth.

b) Find the % of the class that had scores more than one standard deviation above the mean.

c) What is the probability that a score picked at random will fall within one standard deviation of the mean?

a) Enter the grades in L1 and the frequency in L2Press STAT > (CALC) ENTER (1-Var Stats) 2nd L1 , 2nd L2 ENTER

79.5

11.7

X

b) One standard deviation above the mean would be any grade higher than 91.2 (79.5 + 11.7). There are 6. 6

20%30

c) Within one standard deviation of the mean would be any grade higher than 91.2 (79.5 + 11.7) or lower than 67.8 (79.5 - 11.7). There are 15.

15 130 2

Standard Normal Curve

X 1X 2X 3X 1X 2X 3X

68.2%

95.4%

99.8%

Percentiles50th 84th 97th 99th16th2nd0.1st

Standard Normal Curve ExampleThe mean score on a standardized test was 483, and the standard deviation was 97. If 10,000 students took the test, approximately how many students had scores from 386 to 580?

483 580386

68.2%

.6810 2( )( ) 6,0 0 00 ,82

Approximately 6,820 students had scores from 386 to 580.

That was easy