STATISTICS

Statistics is a branch of science, which deals with the collection, presentation, analysis & interpretation of quantitative data.

A.   Branches of Statistics

1.)Descriptive Statistics. A method concerned with collecting, describing, and analyzing a set of data without drawing conclusions (inferences) about a large group.

2.)Inferential Statistics. A branch of statistics, concerned with the analysis of a subset of data leading to predictions or inferences about the entire set of data

 B.   Frequency Distribution. Is a tabular arrangement of data into appropriate categories showing the number of observations in each categories or group.

There are two major advantages:

(a) It encompasses the size of the table;

(b) It makes the data more interpretive.

C.   Parts of Frequency Table

1.)  Class limit- is the groupings of categories defined by the lower & upper limit.

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

3.) Class Boundaries- are the numbers used to separate each categories in the frequency distribution but without gaps created by the class limits.

4.)  Class Marks- are the midpoint of the lower & upper class limits.

Measure of Central Tendency

 There are three commonly used measures of central tendency. These are Mean, Median and Mode.

1 MEAN- it is the most commonly used measure of the center of data.

Mean for Grouped Data

Grouped Data- are the data or scores that are arranged in a frequency distribution.

 Frequency Distribution- is the arrangement of scores according to category of classes including the frequency.

Frequency- is the number of observations falling in a category.

Properties of the Mean

1.)  It measures stability.

2.)   The sum of each score’s distance from the mean is zero.

3.)   It is easily affected by the extreme scores.

4.)   It may not be an actual score in the distribution.

5.)   It can be applied to interval level of measurement.

6.)   It is very easy to compute.

When to use the Mean

1.)  Sampling stability is desired

2.)  Other measures are to be computed such as standard deviation, coefficient of variation and skewness.

2.Median- is the second type of measures of central tendency. Median is what divides the scores in the distribution into two equal parts. Fifty percent (50%) lies below the median value and 50% lies above the median value.

Median of Ungrouped Data

Determine the middle most score in a distribution if n is an add number and get the average of the two middle most scores if n is an even number.

Properties of the Median

1.    It may not be an actual observation in the data set.

2.    It can be applied in ordinal level.

3.    It is not affected by extreme values because median is a positional measure.

When to use the Median

1. The exact midpoint of the score distribution is desired.

2. There are extreme scores in the distribution.

3. Mode- third measure of central tendency

3 Classification of Mode

1. ·         Unimodal – distribution of scores that consist of only one mode.
2. ·         Bimodal- distribution of scores that consist of only two modes.
3. ·         Trimodal- distribution of scores that consist of three modes or multimodal is a distribution of score that consist of more than two modes.

Properties of the Modes

1.)  It can be used when the data are qualitative as well as quantitative.

2.)  It may not unique

3.)  It is not affected by extreme values.

4.)  It may not exist.

Quantiles- a score distribution where the scores are divided in different equal parts.

3 kinds of Quintiles

1.    Quartile- a score point that divides the score in the distribution into four equal parts.

2.    Decile- a score point that divides the score in the distribution into ten equal parts.

3.    Percentile- a score point that divides the score in the distribution into hundred equal parts

REFLECTION

                Statistic is an important tool in teaching. It gives you information on how effective you are in classroom teaching and how valid your tests are. Through statistics, you will know how many of your pupils got the high score.

                This will help the teacher to know if her pupils really understand their lessons or if she still needs to tackle or explain it further. It also validates if the teaching methods and techniques of a teacher is effective and has something to do with the performance of her pupils in class.

                With the help of statistics, teachers are able to see if how many percent of her students are struggling in her class.