26
STATISTICS EXERCISE EDUCATIONAL RESEARCH

STATISTICS EXERCISE u EDUCATIONAL RESEARCH. Organizing Data: An Array 19 23 71 56 17 32 95 23 17 95 71 56 32 23 19 17

Embed Size (px)

Citation preview

STATISTICS EXERCISE

EDUCATIONAL RESEARCH

Organizing Data: An Array19 23 71 56 17 32 95 23

17• 95• 71• 56• 32• 23• 23• 19• 17• 17

Array: Quiz Scores 14.75 12 11.5 13.5 14.75 14.75 13

12.5 13.5 14.75 14.75 14.75 13.50 13.50 13.00 12.50 12.00 11.50

2. Frequency (f) - Cumulative frequency (cf) -

Frequency Example 1: Weights

X Tallies f cf 95 1 1 9 71 1 1 8 56 1 1 7 32 1 1 6 23 1 1 2 5 19 1 1 3 17 1 1 2 2

Frequency Example 2: Quiz scores

X Tallies f cf 14.75 1 1 1 3 9 13.50 1 1 2 6 13.00 1 1 4 12.50 1 1 3 12.00 1 1 2 11.5 1 1 1

SUMMATION Weights Quiz scores 95 14.75 71 14.75 56 14.75 32 13.50 23 13.50 23 13.00 19 12.50 17 12.00 17 11.50 353 120.25

Putting it All Together Weights

X f cf fx 95 1 9 95 71 1 8 71 56 1 7 56 32 1 6 32 23 2 5 46 19 1 3 19 17 2 2 34 n = 9 = 353

Putting it All Together Quiz scores

X f cf fx 14.75 3 9 44.25 13.50 2 6 27.00 13.00 1 4 13.00 12.50 1 3 12.50 12.00 1 2 12.00 11.50 1 1 11.50 n = 9 = 120.25

Mean Weights = 353 / 9 = 39.22 Mean Quiz

Scores = 120.25 / 9 = 13.36

Mode (Mo) Weights 95 71 56 32 23 23 19 17 17

Mo = 17 & 23 -- bimodal

Mode Quiz Scores 14.75 14.75 14.75 13.50 13.50 13.00 12.50 12.00 11.50

Mo = 14.75

3. Median (Mdn) Group A Group B X X 7 50 6 6 5 5 4 -- Mdn 4 -- Mdn 3 3 2 2 1 0

Situations where calculating the median will NOT be so easy. Consider:

7 7 7 8 8 8 9 9 10 10

Mdn = L +[ ( n / 2 - cfb) / fw) } i

7.5 + { ( 10 / 2 - 3 ) / 3 } 1 = 7.5 + (5 - 3) / 3} 1 = 7.5 + (2 / 3) 1 = 8.17

E. Measures of Variability 1. Range

R = Xh - Xl Example 1: Weights R = 95 - 17 = 78 Example 2: Quiz Scores R = 14.75 - 11.5 = 3.25

Deviation Scores x (little x) = X (test score) -

Mean

Example 1: Weights

Score X X - Mean x2 95 55.78 3111.41 71 31.78 1009.97 56 16.78 281.57 32 -7.22 52.13 23 -16.22 263.09 23 -16.22 263.09 19 -20.22 408.85 17 -22.22 493.73 17 -22.22 493.73 n = 9 x2=6377.57 Sum = 353 Mean = 39.22

Example 2: Quiz Scores X X - Mean x2 14.75 1.39 1.93 14.75 1.39 1.93 14.75 1.39 1.93 13.50 0.14 0.02 13.50 0.14 0.02 13.00 -0.36 0.13 12.50 -0.86 0.74 12.00 -1.36 1.85 11.50 -1.86 3.46 n = 9 = 0 x2 =

12.01 Mean = 13.36

Example 1: Weights sigma 2 = 6377.63 / 9 = 708.63

Example 2: Quiz Scores sigma 2 = 12.01 / 9 = 1.33

Example 1: Weights sigma = square root { 63377.63 /

9} = square root {708. 63} = 26.62

Example 2: Quiz Scores sigma = square root {1.33} = 1.15

Standard Scores

z-scores Mean = 0 Standard Deviation

= 1 Equation: z = (X - Mean) /

sigma Mean of raw score distribution sigma = SD of raw score

distribution

b. T-scores Mean = 50 SD = 10 Equation: T = 50 + 10 (z) Example: Let's suppose that a teacher

wants to compare the results of an English and of an Algebra test:

Test Score Mean Highest SD

English 84 110 180 26

Algebra 40 47 60 5

English z-score = ( 84 - 110) / 26

= - 26 / 26 z = - 1.00 Algebra z-score = ( 40 - 47) /

5 = -7 / 5 z = -1.4

English T-score = 50 + 10 (-1.00)

T = 50 + -10 T = 40.00 Algebra T-score = 50 + 10 (-

1.4) T = 50 + -

14.00 T = 36.00

FINISHED--DONE--COMPLETED

AT LONG, LONG LAST