Included in the presentation are definitions of some statistical terms, figures, and mathematical solutions. This is a presentation for Assessment of Learning II.

1. DESCRIBING AND
INTERPRETING TEST
SCORES

5. Score F (Frequency)
20 1
19 1
18 2
17 2
16 7
15 1
14 2
13 0
12 0
11 3
10 5
9 2
8 4
7 2
6 2
5 2
4 0
3 0
2 0
1 0
N= 36

6. Score F (Frequency)
20 1
19 1
18 2
17 2
16 7
15 1
14 2
13 0
12 0
11 3
10 5
9 2
8 4
7 2
6 2
5 2
4 0
3 0
2 0
1 0
N= 36

7. Score F (Frequency)
20 1
19 1
18 2
17 2
16 7
15 1
14 2
13 0
12 0
11 3
10 5
9 2
8 4
7 2
6 2
5 2
4 0
3 0
2 0
1 0
N= 36

8. Score F (Frequency)
20 1
19 1
18 2
17 2
16 7
15 1
14 2
13 0
12 0
11 3
10 5
9 2
8 4
7 2
6 2
5 2
4 0
3 0
2 0
1 0
N= 36

9. Score F (Frequency)
20 1
19 1
18 2
17 2
16 7
15 1
14 2
13 0
12 0
11 3
10 5
9 2
8 4
7 2
6 2
5 2
4 0
3 0
2 0
1 0
N= 36

10. Score F (Frequency)
20 1
19 1
18 2
17 2
16 7
15 1
14 2
13 0
12 0
11 3
10 5
9 2
8 4
7 2
6 2
5 2
4 0
3 0
2 0
1 0
N= 36

11. Score F (Frequency)
20 1
19 1
18 2
17 2
16 7
15 1
14 2
13 0
12 0
11 3
10 5
9 2
8 4
7 2
6 2
5 2
4 0
3 0
2 0
1 0
N= 36

15. 7
6
5
4
3
2
1
0
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

16. 7
6
5
4
3
2
1
0
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

17. 7
6
5
4
3
2
1
0
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Histogram
FrequencyPolygon

18. 7
6
5
4
3
2
1
0
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Histogram
FrequencyPolygon

22. 7
6
5
4
3
2
1
0
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

23. 7
6
5
4
3
2
1
0
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

24. symmetry

25. skewness

26. modality

27. kurtosis

28. Symmetric curve

29. skewness

30. Skewed curves

31. Anatomy of a
skewed curve

32. Anatomyof a skewed curve

33. Anatomyof a skewed curve

34. Anatomyof a skewed curve

36. Anatomyof a skewed curve

37. Positively skewed

38. negatively skewed

39. SKEWED DISTRIBUTION

40. modality

41. modality

42. modality

43. kurtosis

44. kurtosis

45. kurtosis

46. kurtosis

49. Three measures of central tendency are commonly
used in statistical analysis:
mode, median, mean
Each measure is designed to represent a typical
score
which measure to use depends on:
• the shape of the distribution (whether normal or
skewed), and
• the variable’s “level of measurement” (data are
nominal, ordinal or interval).

50. Central Tendency: Mode (p.266)
• Most Common Outcome
• Most frequent score
• The test score which occurs the most
number of times
Find the mode of the following test scores:
a) 7, 13, 18, 24, 9, 3, 18
b) 8, 11, 9, 14, 9, 18, 18, 6, 9, 18
c) 3, 5, 7, 10, 1, 12, 14

51. • Middle-most Value
• 50% of observations are above the Median,
50% are below it
• The difference in magnitude between the
observations does not matter
• Therefore, it is not sensitive to outliers
• Formula Median = n + 1 / 2
Central Tendency: Median (p.265)

52. To compute the median
· first you rank order the values of X from low to
high:  85, 94, 94, 96, 96, 96, 96, 97, 97, 98
· then count number of observations = 10.
· add 1 = 11.
· divide by 2 to get the middle score the 5.5
score (you get the position of the median)
Median = 5th + .5 (6th-7th)

53. • Find the Median
4 5 6 6 7 8 9 10 12
• Find the Median
5 6 6 7 8 9 10 12
• Find the Median
5 6 6 7 8 9 10 100,000
Central Tendency: Median (p.265)

54. • Most common measure of central
tendency
• Best for making predictions
• Applicable under two conditions:
1. scores are measured at the interval level,
and
Central Tendency: Mean-Average (p.264)

55. 2. distribution is more or less normal
[symmetrical
Symbol:
for the mean of a sample
for the mean of a population
Central Tendency: Mean-Average (p.264)

56. Finding the Mean
X = (Σ X) / N
If X = {3, 5, 10, 4, 3}
X = (3 + 5 + 10 + 4 + 3) / 5
= 25 / 5
= 5

57. Appropriate Measures of Central Tendency
• Nominal variables Mode
• Ordinal variables Median
• Interval level variables Mean
- If the distribution is normal (median
is better with skewed distribution)

58. Mode
• Most Common Outcome
• Most frequent score
• The test score which occurs the most
number of times
Male Female

59. IF THE DISTRIBUTION IS NORMAL
Mean is the best measure of central
tendency
•Most scores “bunched up” in middle
•Extreme scores less frequent  don’t
move mean around.

60. Normal distribution

62. Let’s
review

69. references
Raagas, Ester (2015). Assessment and Evaluation of Student Learning:
Concepts and Applications (4th edition).ELR DATStat Analysis Center,
Cagayan de Oro City.
Buenicho, F. C. (2013). Assessment of Student Learning 1. Rex Bookstore:
Manila, Philippines.
Gabuyo, Y. A. (2012) Assessment of Learning I Textbook and Reviewer. Rex
Bookstore: Manila, Philippines
Greenstein, Laura. (2012). Assessing 21st Century Skills. Corwin A SAGE
Company: United States of America.

70. references
Kubiszyn, T. and Borich, G. (2007) Educational Testing and Measurement
Classroom Application and Practice. (8th Ed.). Wiley Jossey-
Bass,Inc. :New Jersey.
Salkind, Neil J. (2013). Tests & Measurement for People Who (Think They)
Hate Tests & Measurement. (2nd Ed.). Corwin A SAGE Company:
United States of America.
Thomas, Laura R. (2013). Facilitating Authentic Learning Grades 6-12.
Corwin A SAGE Company: United States of America.

71. Thank you!
Namaste!