### 1. Displaying Data

Frequency is term that is used to describe common sense of tallying procedure, it to indicate how many people did the same thing on a certain task or how many people have a certain characteristic or in a certain set categories. It provides one way to summarize data and thereby reveal pattern that might not otherwise be noticed. The frequency distribution is frequency of score values are arranged from high to low score. Cumulative frequency can be viewed as the number of student who scored at or below the score in question. The cumulative percentage is the same thing but exprexced as a percentage of total number of student.

Graphic display frequency, Usually frequency displayed in a histogram, a bar graph, or a frequency polygon

### 2. Scale of measure

#### Nominal Scale

It is used for categorizing and naming group, most language teaching professional will sometimes need to categorize language student into group, such as gender, nationality, native language, educational background, socio-economic status, level of language study, membership in particular language class or even whether or not the student say that they enjoy language study.

#### Ordinal Scale

An ordinal scale names a group of observation, but as its label implies, an ordinal scale also order, or rank the data. Example, we rank student from best to worst in some ability based on test that have administered to them.

#### Continuous Scale

It represent the ordering or a named group of data, but they provide additional information, a continuous scale are also shows the distances between the points in the rank, example, language test scores are usually on continuous scale.

### 3. Descriptive statistic

It are numerical representations of how a group of student of student performed on a test, generally test developers are responsible for providing descriptive statistics, so also that all result users can create al mental picture of how the students performed on the test.

### 4. Central tendency

There are several measures of central tendency to the sttistician’s phrase. Two of these are so commonly used in testing, median and arithmetic mean or mean.

Mean is probably the single most often reported in indicator of central tendency. When working with large number of scores, the statistician uses shortcut procedures to determine the mean or median.

Mode, it is that score which occurs most frequently, a memory device that use to keep the mode straight in my mind is that the mode can mean fashionable, thus the mode would be that score which is most fashionable or the received by the most student.

Median, it is that point below which 50 percent of scores fall and above which 50 percent fall, thus in set of scores 100. 98. 83, 76, 65, 59, 40, the median is 76. Median, is the midpoint of a series of scores when the scores are arranged in ascending order of size. Arithmetic mean or often called mean, is t sum of the separate scores divided by their number.

Mid point, in a set of scores is that halfway between the highest score and the lowest score on the test.

Midpoint= high + low / 2

### 5. Dispersion

With a clear understanding how to examine the central tendency of a set of score, the next step to consider dispersion, or how the individual performance vary from the central tendency

Range, it is number of points between the highest score of a measure and lowest score plus one (one added because the range should include the score o both end)

High and low, the range gives some idea of flow for the score on a test spread along the continuum of possible scores, but it does not show where on the continuum the whole set of score lies.

Standard deviation (SD), is averaging process and as such, it is not affected as much by outliner as range. To provide us an indication of the typical test performance of total group of examinees so we may compare an individual’s performance or we may compare two or more groups in terms of typical performance on a given test. Standard deviation or SD is the most stable “index of variability” (measure of the range of scores) and is customirily employed in statistical reports of test performance. The purposes is an understanding of what the standard deviation should mean to us when we find it in a test report.

In figure 6, Harris book, the standard deviation tells us the test scores are distributed more or less over a broad range. The standard deviation also gives us better basis than simply the mean for interpreting individual scores.

Variant, it is equal to squared value of standard deviation, thus formula for the test varience looks very much like the one for the standard deviation except that both sides of equation are squared.

#### The spreadsheet approach to descriptive statistics

Tendency and dispersion statistic cab be calculate using function in your spreadsheet in excel for the statics. Member of student (N)= count (range), mean= average (range), mode= mode (range), median= median (range, midpoint=(MAX(range0+MIN(range))/2, high= max (range), low= min(range), Standard deviation (the N formula)= STDEVP (range), Standard deviation (the N-1 formula)+STDEV (range), Variance (the N formula) = VARP (range), Variance (the N -1 formula) = VAR (range).

#### Reporting descriptive statistic

What should be included, central tendency and dispersion, central tendency indicate the middle, or typically, score for student who took test, it is indicators come in four form, mean (arithmetic average), mode (most often received), median (score that splits the group 50/50), and midpoint (the score halfway between the highest and lowest score). Test developer provide some indicators of the dispersion of soccer or way individuals varies around the typical behavior of the group. Of both commonly reported, mercifully these statistic di not required any calculation, the students who took the test (N) in one such satatistic.

How should test statistic be displayed, calculate the test developer may find themselves presenting test result to colleagues, to funding agencies or a journal in form of research.

### 6. Percentile ranks

We need more specific data on the ranking of individual test performances. One procedure is to translate all the raw scores into percentile ranks. A subject’s percentile rank indicate the percent of the group hich scored lower on the test than he did. With a knowledge of percentile ranks, we may quickly compile lists of those examinees. Percentile ranks are also useful when we wish to compare the standing of an individual on one test. And by computing percentile ranks, we may develop a set of local norms with individual performances comparing.

Raw scores are simple counting the number of right answers. Raw score also has limited meaning. Give meaning to raw scores are each test we must have some simple method of interpreting raw scores in terms of general performance of some group or groups. One method is is to determine the “average” score on the test. Another is to convert the raw scores into percentile or standard scores.