Jolieto C. Caparida, BPE - SPE

Organization of

Scores

TALLIGRAMis a process of tallying scores in a statistical

table using a tally and a diagram

86 74 66 70 56 69 70 73 66 7481 62

60 76 80 81 67 68 73 63 75 7166 70

Procedure:1.Create a table 0 1 2 3 4 5 6 7 8 9 Total

9 0

8 1 11 1 4

7 111 1 11 11 1 1 10

6 1 1 1 111 1 1 1 9

5 1 1

Total 5 3 1 3 2 1 6 1 1 1 24

The columns stands for the ten´s digit. Look at the distribution of the scores, from highest to lowest. In this example, the highest score has 8 as its ten´s digit and 5 as the ten´s of the lowest score.

The rows stands for the one´s digit; that is from 0 to 9.

2. Tally in the intersection of the column for the tens and the row column for the one´s digitFor example, the first score is 86. Tally in the intersection of 8 and 6. Continue the process until all scores are tallied

When all the scores have been tallied, and the totals for each rows and columns have been made, you have finished a talligram.

Uses of Talligram

It shows the frequency of each score, the number of times a score occurs.

It shows the frequency of scores in each ten´s digit or line of tens; thus facilitating in the arrangement of large number of scores in an ascending or descending order.

Uses of Talligram It is used as an aid in score frequency distribution.

It shows the normalcy and skewness of the distribution.

RANKING

is the position of an observation, score

or individual in relation to the

others in the group according to some characters such as magnitude, quality,

or importance.

RANKING

is the process or method of

determining the relative position of values, measures,

or scores according to some bases such

as magnitude, worth, quality, importance or chronology.

it is an arrangement of values or scores from the highest to

the lowest.

45 56 51 61 39 88 85 61 45 61

72 61 69 61 45 70 72 69 37 69

PROCEDUREArrange the scores in a descending order; that is, from highest to lowest in vertical column

Number the scores consecutively from highest to lowest

PROCEDURE

Assign the ranks. The rank of a score occurring once is the same as its consecutive number. If the score occurs two or more times, add the first and last consecutive numbers of the score and divide the sum by the number of sores that appears the same.

CN Rank CNR

88 1 1 61 11 1185 2 2 61 12 1172 3 3.5 61 13 1172 4 3.5 56 14

1470 5 5 51 15 15

69 6 7 45 16 1769 7 7 45 17 1769 8 7 45 18 1761 9 11 39 19 1961 10 11 37 20 20

ExplanationA score of 88 occurs once; it

has a rank of 1. 72 appears twice. Their consecutive numbers are 3 and 4; the sum is 7; so 7/2 is equal to 3.5. The next score is 70 (occurs once); it follows its consecutive numbers are: 6 + 7 + 8 = 21/3 = 7. A score of 69 has a rank of 7. The same procedure is followed for all other numbers.

USES OF RANKING

It is used to indicate the relative position of a student in a group to which he belongs.

It is used in the computation of correlation of coefficients.

It is used in almost all kinds of tests

It provides for a limited amount of comparison.

Rank symbols cannot indicate the extent of difference between adjacent ranks.

LIMITATIONS OF RANKING

It is limited to what can be done to them mathematically.

Scale symbols can be converted into rank symbols but rank symbols cannot be changed into scale symbols

LIMITATIONS OF RANKING

SCORE FREQUENCY

DISTRIBUTION

A frequency distribution is a

table showing how each score occurred. Each score value is

listed and the number of times it occurred is shown.

Score:

48 32 35 28 20 25 28 36 38 41 35 15

16 19 18 33 34 13 15 36 46 44 41 38

39 19 29 16 44 40 43 48 46 47 43 39

Steps:

1.Find the rangeRange = Highest score –

lowest score48 – 13 = 35 range

2.Decide on the number of intervals or number of step interval

Maximum number = 20Minimum number =

7Ideal number = 10

3.Determine the interval by dividing the range by the number of interval decided

35/10 = 3.5 or 4 size of the interval

4.Put up he class interval, starting with the lowest class interval

The lowest class interval should be the lowest score or the next lower number that is exactly divisible by the size of the class interval.

In the example, our lowest score is 13; however 13 is not divisible by 4 (size of the class interval). The next lower number which is divisible by 4 is 12; therefore the lowest class interval should be 12 – 15.

Score Tally f

48 – 51 ll 244 – 47 llll 540 – 43 llll 536 – 39 llll l 632 – 35 llll 528 – 31 lll 324 – 27 l 120 – 23 l 116 – 19 llll 512 – 15 lll 3

N = 36

GRAPHICAL PRESENTATION

OF DATA

It is often good to present data in

graphical form. A common type of

graphic presentation is called a HISTOGRAM

Freq

uenc

y

side

Scores

ScoresThe score intervals are

shown along the horizontal base line. The

vertical height represents the number

of cases.

Another way of presenting the data is to use the

frequency polygon

two types of distribution as a result of using a frequency polygon.

SymmetricalAsymmetrical

In a symmetrical distribution, each half or side of the distribution is a

mirror image of the other side.

An asymmetrical distribution, has nonmatching side of halves.

An symmetrical distribution results to a skewed distribution.

TWO TYPES OF SKEWNESS

Positive Skewness – indicates that the class did poorly in the test (majority got low in the test).Negative Skewness – indicates that majority have high scores.

Positively skewed

Negatively skewed

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