The word population refers to groups or aggregates of people, animals, objects, materials, happenings or things of any form, this means that there are populations of students, teachers, supervisors, principals, laboratory animals, trees, manufactured articles, birds and many others. If your interest is on few members of the population to represent their characteristics or traits, these members constitute a sample. The measures of the population are called parameters, while those of the sample are called estimates or statistics.
It refers to a characteristic or property whereby the members of the group or set vary or differ from one another. However, a constant refers to a property whereby the members of the group do not differ one another.
Variables can be according to functional relationship which is classified as independent and dependent. If you treat variable y as a function of variable z, then z is your independent variable and y is your dependent variable. This means that the value of y, say academic achievement depends on the value of z.
1. Nominal – this refers to a property of the members of a group defined by an operation which allows making of statements only of equality or difference. For example, individuals can be classified according to thier sex or skin color. Color is an example of nominal variable.
2. Ordinal – it is defined by an operation whereby members of a particular group are ranked. In this operation, we can state that one member is greater or less that the others in a criterion rather than saying that he/it is only equal or different from the others such as what is meant by the nominal variable.
3. Interval – this refers to a property defined by an operation which permits making statement of equality of intervals rather than just statement of sameness of difference and greater than or less than. An interval variable does not have a “true” zero point.; althought for convenience, a zero point may be assigned.
4. Ratio – is defined by the operation which permits making statements of equality of ratios in addition to statements of sameness or difference, greater than or less than and equality or inequality of differences. This means that one level or value may be thought of or said as double, triple or five times another and so on.
3. Experimental method – a method designed for collecting data under controlled conditions. An experiment is an operation where there is actual human interference with the conditions that can affect the variable under study.
4. Use of existing studies – that is census, health statistics, weather reports.
5. Registration method – that is car registration, student registration, hospital admission and ticket sales.
Frequency Distribution is defined as the arrangement of the gathered data by categories plus their corresponding frequencies and class marks or midpoint. It has a class frequency containing the number of observations belonging to a class interval. Its class interval contain a grouping defined by the limits called the lower and the upper limit. Between these limits are called class boundaries.
Frequency of a Nominal Data Male and Female College students Major in Chemistry 130 TOTAL 107 FEMALE 23 MALE FREQUENCY SEX
Frequency of Ordinal Data Ex. Frequency distribution of Employee Perception on the Behavior of their Administrators 100 total 31 Strongly unfavorable 22 Unfavorable 14 Slightly unfavorable 12 Slightly favorable 11 favorable 10 Strongly favorable Frequency Perception
Compute the range: R = H – L and the number of classes by K = 1 + 3.322log n where n = number of observations.
Divide the range by 10 to 15 to determine the acceptable size of the interval. Hint: most frequency distribution have odd numbers as the size of the interval. The advantage is that the midpoints of the intervals will be whole number.
Organize the class interval. See to it that the lowest interval begins with a number that is multiple of the interval size.
2. Histogram or bar graph- this graphical representation can be used in nominal, ordinal or interval. For nominal bar graph, the bars are far apart rather than connected since the categories are not continuous. For ordinal and interval data, the bars should be joined to emphasize the degree of differences
Given the bar graph of how students rate their library.
A-strongly favorable, 90
C-slightly favorable, 88
D-slightly unfavorable, 48
F-strongly unfavorable, 25
The Histogram of Person’s Age with Frequency of Travel 100% 51 total 3.9% 2 27-28 7.8% 4 25-26 7.8% 4 23-24 41.2% 21 21-22 39.2% 20 19-20 RF freq age
Quartiles refer to the values that divide the distribution into four equal parts. There are 3 quartiles represented by Q 1 , Q 2 and Q 3 . The value Q 1 refers to the value in the distribution that falls on the first one fourth of the distribution arranged in magnitude. In the case of Q 2 or the second quartile, this value corresponds to the median. In the case of third quartile or Q 3 , this value corresponds to three fourths of the distribution.
Percentile- refer to those values that divide a distribution into one hundred equal parts. There are 99 percentiles represented by P 1 , P 2 , P 3 , P 4 , P 5 , …and P 99 . when we say 55 th percentile we are referring to that value at or below 55/100 th of the data.