utilization of data: introduction to statistics

CHAPTER 5UTILIZATION OF ASSESSMENT DATA

CHRISTINE P. MEJINOBSEd III-A English

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.

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

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.

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

DESCRIPTIVE STATISTICS

• 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

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

FREQUENCY DISTRIBUTION

A. It encompasses the size of the table.B. It makes the data more interpretative.

ADVANTAGES OF FREQUENCY DISTRIBUTION

1. Class limit is the groupings or categories defined by the lower or upper limits.

PARTS OF FREQUENCY TABLE

ExampleLower 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.

2. Class Size (c.i) is the width of each class interval.

ExampleLower 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

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

4. Class Marks are the midpoint of the lower and upper class limits. The formula is

Lower limits(LL)

Upper limits(UL)

10 14 12

15 19 17

20 24 22

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

𝑐 .𝑖= 𝑅𝑑𝑒𝑠𝑖𝑟𝑒𝑑𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑐𝑙𝑎𝑠𝑠𝑒𝑠 𝑜𝑟 𝑐 . 𝑖=𝑅

𝑘

(5, 10, 15)

R=HS-LS

k=1+3.3 log n

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.

3. Set up the class boundaries if needed. Use the formula:

4. Tally the scores in the appropriate classes.

5. Find the other parts if necessary such as class marks, among others.

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 1927 35 45 48 20 38 39 1844 22 46 26 36 29 15 2150 47 34 26 37 25 33 4922 33 44 38 46 41 37 32

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).

17 25 30 33 25 45 23 1927 35 45 48 20 38 39 1844 22 46 26 36 29 15 2150 47 34 26 37 25 33 4922 33 44 38 46 41 37 32

15-20

21-26

27-32

33-38

39-44

45-50