This document discusses key concepts in utilizing assessment data through statistics. It defines statistics as dealing with quantitative data collection, presentation, analysis and interpretation. Descriptive statistics describe data without inferences, while inferential statistics allow predictions about a larger data set from a sample. Frequency distributions tabulate data into categories to make it more interpretable. They include class limits, size, boundaries, and marks. Steps for constructing distributions include determining the range, class size, limits, boundaries, tallying scores, and identifying other parts. An example constructs a distribution from exam scores using these steps.

1. CHAPTER 5
UTILIZATION OF ASSESSMENTDATA
CHRISTINE P. MEJINO
BSEd III-A English

2. STATISTICS
• It is an important tool in the utilization of the assessment data most
especially in describing, analyzing, and interpreting the performance of the
students in the assessment procedures.

3. DEFINITION OF STATISTICS
• Is a branch of science, which deals with the collection,
presentation, analysis, and interpretation of quantitative data.
Collection Presentation Analysis Interpreta-tion

4. STATISTICAL QUESTION
• A question where you expect to get a variety of
answers, and you are interested in the distribution and
tendency of those answers.

5. • Is a method concerned with collecting, describing and
analyzing a set of data without drawing conclusions (or
inferences) about a large group.
DESCRIPTIVE STATISTICS

6. • Is a branch of statistics, concerned with the analysis of
a subset of data leading to predictions or inferences
about the entire set of data.
INFERENTIAL STATISTICS

8. • Is a tabular arrangement of data into appropriate
categories showing the number of observations in each
category or group.
FREQUENCY DISTRIBUTION

9. A. It encompasses the size of the table.
B. It makes the data more interpretative.
ADVANTAGES OF FREQUENCY
DISTRIBUTION

10. 1. Class limit is the groupings or categories defined by the lower
or upper limits.
PARTS OF FREQUENCY TABLE

11. Example
Lower limits
(LL)
Upper limits
(UL)
10 14
15 19
20 24
• Lower class limit (LL) represents the smallest number in each group.
• Upper class limit (UP) represents the highest number in each group.

12. 2. Class Size (c.i) is the width of each class interval.
Example
Lower limits
(LL)
Upper limits
(UL)
10 14
15 19
20 24
The class size in this score distribution is 5.
11-12-13
16-17-18
21-22-23

13. 3. Class Boundaries are the numbers used to separate each category in
the frequency distribution but without gaps created by the class limits.
The scores of the students are discrete. Add 0.5 to the upper limit to get
the upper class boundary and subtract 0.5 to the lower limit to get the
lower class boundary in each group or category.
Lower limits
(LL)
Upper limits
(UL)
10 14
15 19
20 24
LCB UCB
9.5 14.5
14.5 19.5
19.5 24.5

14. 4. Class Marks are the midpoint of the lower and upper class limits.
The formula is 𝑋 𝑚 =
𝐿𝐿+𝑈𝐿
2
Lower limits
(LL)
Upper limits
(UL) 𝑋 𝑚
10 14 12
15 19 17
20 24 22

15. 1. Compute the value of range (R).
RANGE is the difference between the highest score and the lowest score.
Determine the class size (c.i). The class size is the quotient when your divide the
range by the desired number of classes or categories. The desired numbers of classes are
usually 5, 10 or 15 and they depend on the number of scores in the distribution. If the desired
number of classes is not identified, find the value of k, where k= 1+3.3 log n.
STEPS IN CONSTRUCTING FREQUENCY
DISTRIBUTION
R= HS-LS

16. 𝑐. 𝑖 =
𝑅
𝑑𝑒𝑠𝑖𝑟𝑒𝑑 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑐𝑙𝑎𝑠𝑠𝑒𝑠
𝑜𝑟 𝑐. 𝑖 =
𝑅
𝑘
(5, 10, 15)
R=HS-LS
k=1+3.3 log n

17. 2. Set up the class limits of each class or category. Each class defined by the
lower limit and upper limit. Use the lowest score as the lower limit of the
first class.

18. 3. Set up the class boundaries if needed. Use the formula:
𝑐𝑏 =
𝐿𝐿 𝑜𝑓 𝑡ℎ𝑒 𝑠𝑒𝑐𝑜𝑛𝑑 𝑐𝑙𝑎𝑠𝑠 − 𝑈𝐿 𝑜𝑓 𝑡ℎ𝑒𝑓𝑖𝑟𝑠𝑡 𝑐𝑙𝑎𝑠𝑠
2
4. Tally the scores in the appropriate classes.
5. Find the other parts if necessary such as class marks, among
others.

19. EXAMPLE:
• Raw scores of 40 students in a 50-item Mathematics quiz. Construct a frequency
distribution following the steps given previously.
17 25 30 33 25 45 23 19
27 35 45 48 20 38 39 18
44 22 46 26 36 29 15 21
50 47 34 26 37 25 33 49
22 33 44 38 46 41 37 32

20. Construct the class limit starting with the lowest score as the lower limit of the first
category. The last category should contain the highest score in the distribution.
Each category should contain 6 as the size of the width (X). Count the number of
scores that falls in each category (f).

21. 17 25 30 33 25 45 23 19
27 35 45 48 20 38 39 18
44 22 46 26 36 29 15 21
50 47 34 26 37 25 33 49
22 33 44 38 46 41 37 32
15-20
21-26
27-32
33-38
39-44
45-50