Friday, October 8, 2010
Graphical Representation
Graphical Representation:
Graphical representation is necessary in the field of education. To understand data and draw conclusion is possible. To make data simple and comprehensive.
Three types of graphical representation:
1. Histogram
2. Frequency Polygon
3. Cumulative Frequency Curve
4. Ogive
Points in preparing graph:
In graph X – axis is abscissa and y axis is ordinate. Class interval is on x –axis. Frequencies on y –axis. Meeting point of X & Y axis is always taken as zero. Scale should be sufficiently large. It is advisable to take convenient units to show on X & Y axis.
A) Histogram:
In statistics a histogram is a graph that represents the class frequencies in frequency distribution by vertical rectangles.
- Simpson & Kalfk
Points to be kept in mind for histogram:
1. X – axis represents class intervals.
2. Y – axis represents frequencies
3. Height of every rectangle is according to the frequencies of the class interval which it represent.
When to use it?
When you want to see the pattern of variation of a particular process, such as when you are describing a problem, or during data collection and analysis.
The steps to create a histogram include:
- Gather the data about the variable you are interested in.
- Look at the data and determine the categories or intervals you will use to organize the data. For example, if you are measuring the number of weeks it takes to receive an order of contraceptives, "number of weeks of waiting time" is the data category.
- Construct a frequency table for your data. The frequency corresponds to the number of times each value is observed. Using the example of waiting time to receive an order of contraceptives, the frequency table might look like this:
- To create the histogram, draw a horizontal and a vertical axis. The horizontal axis (X) shows the data categories (such as time, or a measurement, like weight). The vertical axis (Y) represents the frequency of the observations (the number of observations for each category).
- For each category of data, draw a rectangle (without space between the rectangles). The width of the rectangle represents the interval between two groups, and the height represents the observed frequency.
When class interval is inclusive convert it into exclusive series
B) Frequency Polygon:
Polygon means many angles. Figure which depicts frequency is called frequency polygon. Plain figure bounded by a number of straight line a figure of many angles. Midpoint is on X –axis and Frequency on Y – axis. Two extra class intervals are assumed. One on top with zero frequency and another on bottom with zero frequency. Frequencies of this class interval is shown with dotted line.
Steps for preparing Frequency Polygon:
1. Assume two extra class intervals with zero frequency.
2. Find midpoint of each class interval.
3. Plot midpoint on X- axis.
4. Plot frequencies on Y- axis.
5. Join this points with straight line.
6. Then join this with the base on midpoints of assumed class intervals.
Statistical methods and data interpretation
Statistical Methods & Interpretation of Scores:
Need statistics in educational evaluation:
1. To know students achievement
2. To know overall school achievement
3. To improve quality in education
4. To find out the status in education through educational research
5. To understand the data and drawing conclusion
Importance of Statistics in Educational Evaluation:
1. To study students average attendance
2. To study the comparison of result among individuals
3. To study the comparison of result between two groups
4. To study the correlation between two groups
5. To study the position of student in group in terms of the percentage of individual which are below him.
Tabulation of Data:
1. To understand the nature of acquired data
2. To accept them data are to be organized. Three methods to organize data:
- Classification
- Tabulation
- Presentation in graphic form
Scores are organize in three ways:
- Simple Array
- Frequency Array
- Frequency Distribution
A) Simple Array:
1. Simplest way to organize data
2. Used when number of scores is small (20)
3. Not used for repeated scores in obtained data
4. Scores are arranged in ascending & descending order.
Example:
Raw scores Ascending order Descending Order
6 10 2
8 9 3
5 8 4
4 6 5
2 5 6
9 4 8
10 3 9
B) Frequency Array:
Repeated scores in obtained data
Example:
Scores of 20 individuals age is given below
13,12,12,12,12,11,11,11,11,11,11,11,11,10,10,10,10,10,9,9
These scores can be organized in the following way
13
12,12,12,12
11,11,11,11,11,11,11,11
10,10,10,10,10
9,9
Above information is not clear
Thus better way to organize data is
Age Tallies Frequencies
13 | 1
12 | | | | 4
11 | | | | | | | | 8
10 | | | | | 5
9 | | 2
__________
N = 20
C) Frequency Distribution:
An organization of measures or observations into score classes along with the frequency in each class is called frequency distribution.
Frequency distribution method is used when number of scores is too many. Scores repeated several times. Observations are divided into subgroups. Frequencies are depicted in front of each sub group
Steps for preparing frequency distribution:
1. Find out highest & lowest numbers & difference between these two scores i.e. range
Formula is Range = Highest score/ number – Lowest score / number
2. Determine number of class interval. It should between 5 to 20 depending on the range of scores.
3. Determine size of class interval. It should be neither too big nor too small. Should be in odd number if possible.
Formula Size of class interval = Range / No .of class interval
4. Determine number of class interval.
Formula No. of class interval = Range / Size of class interval
5. Scores arranged in the classes
6. Prepared class interval in such a way that the lowest number of scores should be the midpoint of first class interval.
7. Limit of class interval should be multiple of 5
8. Add size of class interval to each value of the first class interval, the next class interval can be obtained.
9. Class intervals can be written in either ascending or descending order.
10. Mark tallies against each class interval.
Statistical methods and data interpretation
Statistical Methods & Interpretation of Scores:
Need statistics in educational evaluation:
1. To know students achievement
2. To know overall school achievement
3. To improve quality in education
4. To find out the status in education through educational research
5. To understand the data and drawing conclusion
Importance of Statistics in Educational Evaluation:
1. To study students average attendance
2. To study the comparison of result among individuals
3. To study the comparison of result between two groups
4. To study the correlation between two groups
5. To study the position of student in group in terms of the percentage of individual which are below him.
Tabulation of Data:
1. To understand the nature of acquired data
2. To accept them data are to be organized. Three methods to organize data:
- Classification
- Tabulation
- Presentation in graphic form
Scores are organize in three ways:
- Simple Array
- Frequency Array
- Frequency Distribution
A) Simple Array:
1. Simplest way to organize data
2. Used when number of scores is small (20)
3. Not used for repeated scores in obtained data
4. Scores are arranged in ascending & descending order.
Example:
Raw scores Ascending order Descending Order
6 10 2
8 9 3
5 8 4
4 6 5
2 5 6
9 4 8
10 3 9
B) Frequency Array:
Repeated scores in obtained data
Example:
Scores of 20 individuals age is given below
13,12,12,12,12,11,11,11,11,11,11,11,11,10,10,10,10,10,9,9
These scores can be organized in the following way
13
12,12,12,12
11,11,11,11,11,11,11,11
10,10,10,10,10
9,9
Above information is not clear
Thus better way to organize data is
Age Tallies Frequencies
13 | 1
12 | | | | 4
11 | | | | | | | | 8
10 | | | | | 5
9 | | 2
__________
N = 20
C) Frequency Distribution:
An organization of measures or observations into score classes along with the frequency in each class is called frequency distribution.
Frequency distribution method is used when number of scores is too many. Scores repeated several times. Observations are divided into subgroups. Frequencies are depicted in front of each sub group
Steps for preparing frequency distribution:
1. Find out highest & lowest numbers & difference between these two scores i.e. range
Formula is Range = Highest score/ number – Lowest score / number
2. Determine number of class interval. It should between 5 to 20 depending on the range of scores.
3. Determine size of class interval. It should be neither too big nor too small. Should be in odd number if possible.
Formula Size of class interval = Range / No .of class interval
4. Determine number of class interval.
Formula No. of class interval = Range / Size of class interval
5. Scores arranged in the classes
6. Prepared class interval in such a way that the lowest number of scores should be the midpoint of first class interval.
7. Limit of class interval should be multiple of 5
8. Add size of class interval to each value of the first class interval, the next class interval can be obtained.
9. Class intervals can be written in either ascending or descending order.
10. Mark tallies against each class interval.
Tools of evaluation
Tools of Evaluation:
1. Observation:
Meaning: It is an instrument of assessing personality. To measure things very minutely.
Definition: Measurement without instrument is called observation.
Examples:
1. Teachers have listened to speeches & ranked student 1, 2, 3
2. Students have been labeled good, fair or poor in achievement & lazy or diligent in study.
3. Farmers feel the breeze watching sky.
4. Physicians observe of the patients talk, gestures & facial expressions.
Merits of Observation:
1. Valuable supplementary information can be provided.
2. Reliable & objective
3. Study of an individual in a natural situation
4. Used with children of all ages
5. Used with training & experience
6. Adaptable to both individual & groups
7. Students work and students habit can be observed
Limitations / Demerits of Observation:
1. Personal prejudice and bias of the observer
2. No accurate observation is noted
3. Difficult to observe small behaviour of the students
4. Reveals the overt behaviour only
Principles to be followed in making observation:
1. Observe whole situation
2. Select one student to observe
3. Observe in their regular activities
4. Observation should be made over a period of days
5. Collect observations from several teachers
Requisites of good observation:
1. Proper planning
Define specific activities or units of behaviour clearly. Select appropriate group of subjects. Decide time period for the observation, form of recording and instrument use for recording. Decide physical position too.
2. Proper execution:
Arrange special conditions. Execute observation at decided physical position. Focus attention. Observe discreetly. Properly handle recording instrument to record observation. Utilize training received in terms of expertness.
3. Proper Recording:
Depend upon the nature of activities or behaviour of the group to observe. It is depend on two methods.
1. Simultaneous observation: Time gap may distract fact. May be able to recall
2. After observation: Time gap do not distract fact. May not able to recall.
Devices used in observation are checklist, rating scale, score cards and blank form of tallying frequency.
4. Proper Interpretation:
Interpret observation cautiously and judiciously. See that limitations of planning, sampling or procedure may give wrong interpretation.
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