4.1: Mean

Mean - the sum of all the measurements in a data set divided by the number of measurements in the set; the symbol for mean is .

Although text, tables and graphs effectively present data, these do not sufficiently describe the data being presented.

Measures of Central Tendency - numerical descriptive measures which indicate the center of a data set

There are three commonly used measures of central tendency:

3.3 Graphical Method

Presenting data using the graphical method facilitates the easy comparison and interpretation of data without having to go through numerical data.

Types of Charts:
Bar Chart - represented by either vertical or horizontal rectangles whose bases represent the class intervals and whose heights represent frequencies

Examples: {Click on image to see full-sized chart.}

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Data can also be presented by using tables. Important features and significant values are easily observed when data are presented in a tabular form. Moreover, comparisons are also easily made.

Parts of a Table:

1. Table number - for easy reference to the table
2. Table title - briefly explains the content of the table
3. Column header - describes the data in each column
4. Row classifier - shows the classes or categories
5. Body - main part of the table
6. Source note - placed below the table when the data presented are not original

Example:

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The TEXTUAL METHOD is used when ungoruped data is presented in a paragraph form. The paragraph or text presents (usually through enumeration) the important characteristics of the data. It also gives emphasis to significant figures (or values) and important features of the data such as trends, irregularities and extreme values, if any.

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In order to see or observe the significant characteristics of a data set, it must be presented in an organized and systematic way. There are three ways to present data: textual, tabular, and graphical.

There are two ways of classifying data: grouped and ungrouped.

Ungrouped data - not organized; if arranged, could only be from highest to lowest or lowest to highest

Grouped data - organized and arranged into different classes or categories

Example:
A simple list of the birthdays of the students of a section is ungrouped data even if it arranged from first to last or last to first. But if it is listed by month, it is grouped data.

A SAMPLING TECHNIQUE is a procedure used to determine the indiciduals or members of a sample. It may be a probability or non-probability sampling technique.

Probability Sampling - each member ir element of the population has an equal chance of being selected as members of the sample

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In research, the entire population is seldom used because of the cost and time involved. Most researches use only a small representative of a population called the sample. The sample is used to know and/or describe the characteristics of a population.

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COLLECTING DATA is the first step in conducting a research or study. It may be gathered from primary or secondary sources.

Primary Sources - statistical data from government institutions, business agencies, civil society organizations, first-hand surveys and interviews

Secondary Sources - books, encyclopedia, journals, magazines, research or studies by other people

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SUMMATION NOTATION or SUMMATION (Σ) is the most common symbol used in statistics.

In statistics, variables are represented by using capital letters.

Example:
If we want to represent the age of 40 students in a class, the age of the first student is represented by X₁, the age of the second student is X₂, the age of the third student is X₃, and so on until X₄₀. The sum of the ages can be expressed in this way:

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