Basic Statistics

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Page 1 of 17

1. 2. 3.

1. 2. 3. 4. 5. 1. 1. 2 . 3. 2. 2 1. 2. 3. 3.1 3.1.1 3.1.2 3.1.3 3.2 2 3.2.1 3.2.2 3. 3 t-test one-Group 3. 4 2 t-test 3.5 2 Analysis of Variance (ANOVA) 3.6 Chi-Square 4. 4.1 4.2 4.3 - (Pictogram) - (Histogram)

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- (Line graphs) - (Ogive Curve) - (Pie Chart) 5.

1. (Percentage) 2. (Measures of Central Tendency) 3. (Measures of Variability) 4. (Measures of Relationship) 1. (Percentage) 100 100 5 530 135 124 90 50 75 56 = 135/530 x100 = 25.47 = 124/530 x 100 = 23.39 = 90/530 x 100 = 16.98 = 50/530 x 100 =9.43 = 75/530 x 100 = 14.15 = 56/530 x 100= 10.56 100

1

- - - - - 1-5 - 6 10 3 18.7 - 10 5 31.3 . - 1 5

4 12 12 4 8 3 5

25.0 75.0 75.0 25.0 50.0 18.7 31.3

14

87.5

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- 6 10 - 10 - - -

2 1 15

12.5 6.2 93.8

1 ( 75) ( 75) 1 5 ( 50) . 1 5 ( 87) ( 93.8)

2 .011 48 64 40 80 30 70 30 112 30 28 24 52 20 40 15 45 15 56 15 14 24 28 30 40 80 40 100 36 20 52 12 14 15 20 40 20 50 18 10 26 16 18 10 20 30 30 50 18 30 100 8 9 5 10 15 15 25 14 15 50

-

112 90 120 60 60 40 20 24 120 20 56 25 60 30 30 20 10 12 60 10

2 .011 -

1. 100 .4 150 60 90 38 70 = 38/60 x 100 = 63.33 = 70/90 x 100 = 77.77 = 108/150 x 100 = 72 2. 1 63.33% 77.77% (63.33% 60 77.77% 90) 3. .. 2541 100 % 2 4. 100 250% 2.50 5. Print-out 2

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Cell (row) (Colomn)

- 186 (38.83%) 211 (37.68%) 141 (32.68%) 149 (31.11%) 184 (32.86%) 145 (33.64%) 36 85 (7.51%) (17.75%) 45 102 (8.04%) (18.21%) 43 90 (9.98%) (20.88%) 277 (18.84%) 19 (3.97%) 13 (2.32%) 8 (1.86%) 40 (2.72%) 4 (0.83%) 5 (0.89%) 4 (0.93%) 13 (0.88%) 479 (100%) 560 (100%) 431 (100%) 1,470 (100%)

538 478 124 (36.60%) (32.52%) (8.44%)

2. (Measure of Central Tendency) (Average) 3 1. (Arithmetic Mean) 2. (Median) 3. (Mode) 2.1 (Arithmetic Mean) 2 1. 2. 1 N

=

n N

7 30 35 20 16 17 25 29

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= 24.57 24.57

= =

=

N N = n n =

( ) 12-14 15-17 18-20 21-23 24-26 27-29 30-32

(f) 4 7 9 12 10 5 3 N = 50

(X) 13 16 19 22 25 28 31

fx 52 112 171 264 250 140 93 = 1082

1) (X) 2) X f 3) ( )

=

=

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= 21.64 21.64

1. 2. 0 3+4+5+6+7,

= 5 (3-5)+(4-5)+(5-5)+(6-5)+(7-5)

= (-2)+(-1)+0+1+2 = 0 3. 4.

=

40 50 42 ,36, 40 35 =

4 30,35

= 37.87 37.87

1. 2. 3. 4. t t-test 5. (Normal Curve) 2.2 (Median) 50% 50%

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2.2.1 (Ungrouped Data) 2.2.2 ( grouped Data) 2.2.1

1. 10 12 15 19 21 = = 15 2. 7 , 8 , 10 , 12 ,15 19 =

=

2.2.2

Median (Mdn)=

+

Mdn

F f n i

32-34 29-31 26-28 23-25 20-22 17-19 14-16 11-13 8-10 5 7

31.50-34.50 28.50-31.50 25.50-28.50 22.50-25.50 19.50-22.50 16.50-19.50 13.50-16.50 10.50-13.50 7.50-10.50 4.50-7.50

f 1 2 1 2 7 9 6 4 5 3 40

Cf* 40 39 37 36 34 27 18 12 8 3

*cf =(Cumulative Frequency)

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=

= 20

17-19

(Mdn) =

+

= 16.50 +

= 16.50 + (0.67) = 17.17 17.17

1. 9 11 14 16 20 14 10 13 14 18 20 14 2.

1 15 16 17 19 22 = 17.8 Mdn = 17 2 15 16 17 19 60 = 25.4 Mdn = 17 2 60 1 3. (Mode)

1 2 3 4 4, 5 ,7 ,5 ,2, 5 3, 5, 7, 9, 10, 12 2, 2, 4, 5, 6, 6 3, 3, 8, 7, 3, 8 , 8 (Mo) 5 2 6 3 8

( ) (Mdn) (Mo) Mo = 3 Mdn - 2

2,800 2,900 Mo = 3 Mdn - 2 = 3(2,900) 2(2,800) = 8,700 5,600

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= 3,100 3,100 /

1. 1 2 Bimodal 2 Multimodal 2.

1. (Normal Curve) (Symmetric Curve) (bell shape)

2. (Positively Skewed)

3. (Negative Skewed)

1. (Mean) (Interval Scale) (Ratio Scale) (Extreme Value)

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2. (Median) (Ordinal Scale) () 3. (Mode) (Nominal Scale) 3. (Measure of Variability)

3 3 60 1 80 40 40-80 2 1 1 3 1 2 1 3

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1.3.1 (Range) 1.3.2 (Standard Deviation) 1.3.3 (Variance) 1.3.1 (Range) (Maximum) (Minimum) = R = Max - Min

10 12 9 18 R = max min = 20 6 = 14 =14 1.3.2 (Variance) (degree of freedom)

1.3.3 (Standard deviation)

1.

=

X = =

N = f =

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92-100 83-91 74-82 65-73 56-64 47-55 38-46 29-37 20-28 11-19 2-10 (x) 96 87 78 69 60 51 42 33 24 15 6 (f) 60 140 160 120 140 80 119 81 50 32 18 N=1,000

fx, , 92-100 83-91 74-82 65-73 56-64 47-55 38-46 29-37 20-28 11-19 2-10

, X 96 87 78 69 60 51 42 33 24 15 6

f 60 140 160 120 140 80 119 81 50 32 18

fx 5,760 12,180 12,480 8,280 8,400 4,080 4,998 2,673 1,200 480 108 = 60,639 552,960 1,059,660 973,440 571,320 504,000 208,080 209,916 88,209 28,800 7,200 648 = 4,204,23

N = 1,000

= = = 22.96 = 22.96 2.

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S = X = =

n = f =

50 ( ) 2 3 4 5 6 7 8

2 7 10 15 9 5 2 n = 50

fx, X 2 3 4 5 6 7 8 X2 4 9 16 25 36 49 64

,

f

fx 4 21 40 75 54 35 16 =245 8 63 160 375 324 245 128 =1,303

2 7 10 15 9 5 2 N = 50

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= 1.45 1.45 1. 2. 3. (Coefficient of Variation) 2 =

2 1 35 6 2 40 8

= 1 = 2 = =0.17 =0.20

2 1

4. (Measures 0f Relationship) .3 (Correlation Coefficient ) (Simple Correlation Coefficient) (-1) (+1)

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IQ

IQ 0.87 R2 = 0.7569 (IQ) ( ) 75.69

(IQ) ( ) 75.69 (IQ) ( ) 24.30 (Pearson Product moment

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Correlation Coefficient) (Interval Scale)

N n X 1 Y 2

10 1 2 3 4 5 6 7 8 9 10

(X) (Y)24 21 18 29 15 20 26 28 17 25 = 223 21 18 20 25 18 19 24 23 12 20 = 200 576 441 324 841 225 400 676 784 289 625 = 5,181 441 324 400 625 324 361 576 529 144 400 = 4,124

XY 504 378 360 725 270 380 624 644 204 500 = 4,589

= 223 = 5,181

= 200 = 4,124

= 4,589 n = 10

= 0.80

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1. 2. 2.1 6 8 10 12 20 26 3 6 8 9 5 2 2.2 20-22 23-25 26-28 29-31 32-34 3 8 12 9 2 3. X Y 78101215976 7101310121198

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