Characteristics of Mean:-
1) Each score of the series is affected. If a single score is changed then the mean is changed.
2) Seriously effected by extreme scores on the end of a series.
3) Balancing point of a numerical series because the sum of positive & negative deviations from the mean is always zero.
4) It is an unbiased statistics.
5) If some constant figure is added, subtracted, multiplied or divided to each score of the series, then the mean is also increased or decreased in the same ratio.
6) The sum of positive & negative deviation taken from mean is always zero.
7) The sum of squared deviation taken from the mean is always the minimum.
1) Uses of Mean:-
- Distribution of scores is systematically around all scores.
- When the most stable & reliable measure is required.
- Calculating higher statistics (standard deviation, correlation)
2) Median:-
- Position of median is an arranged series is so that half the score lies above it & half below it.
- Series is divided into the equal halves.
- Midpoint of either ascending or descending arranged series above & below which lies the 50% scores.
Definition:-
“When ungrouped scores or other measures are arranged in order of size then median is the midpoint in the series.”
“The median is defined as that point on the scale of measurement above which are exactly half the cases & below which are the other half.”
Computation of Median:-
- Ungrouped Data:
Mdn = (N + 1/ 2)th item
- Grouped Data:
Mdn = L+ [ N/2 - F/fm] x i
Steps for Ungrouped Data:-
- Arrange scores in ascending or descending order.
- Add one to the number of scores & divide by two.
Steps for Grouped Data:-
- When the data is grouped then the median is 50% point of distribution.
Steps:
- Calculate n/2 ( Half of the total frequencies)
- See that N/2 lies in which class interval.
- ‘L’ will be the exact lower limit of the class interval in which N/2 lies.
- Find out cumulative frequencies below the N/2 class interval (F is the addition of frequencies in each class intervals)
- Find fm which is the frequency of N/2 class interval
- Substitute value of N/2, L, fm, F & I i.e (Length of class interval in which N/2 Lies)
- First subtract N/2 from F then divide by fm. Multiply it with 5 & add to value of L.
Examples:- Solve using formulas for grouped & ungrouped data.
Characteristics of Median:-
- Balancing point in a series, above & below which lies 50% of scores.
- Sum of deviations taken from the median is minimum if signs are neglected.
Uses of Mean:-
-When there are extreme scores in the series
- Actual midpoint of the series is desired.
- When some scores will effect the measure of central tendency, but about them the only information known is that they are situated at the ends of the series.
3) Mode:-
- Most frequent score in a numerical series.
- Value which occurs most frequently in a series.
Computation of Mode:-
1) Ungrouped Data
Frequent Scores
2) Grouped Data
Mode=3Md-2M
Examples:- solve using above formula.
Characterisitics of Mode:-
- Average widely used in everyday life.
- Easily understood & determined by inspection alone.
- Encourages attention to bimodal & multimodal data.
- It appears best to represent the group.
VI - Coefficient of Correlation – Spearman’s Rank difference Method:
Meaning:-
Correlation is concerned with describing the degree of relation between variables.
The degree to which two variables vary together.
Spearman’s Rank difference method – formula
R=1 - 6 sigma D square / n(n2-1)
Where
Sigma D square= is the square of the difference in ranks
N= number of scores
N square = square of n
Steps:-
1) First ranks of x variable are given. One has to observe which is the highest score, it is given first rank & so on. Similarly ranks are given to y variable.
2) To find out the difference of ranks
3) Now square this difference to obtain D square.
4) Now square this value in the formula.
Examples: Solve using the formula
Reference: Measurement & Evaluation in psychology & Education by Dr Bipin Asthana.
Unit 2: Tools & Techniques of Evaluation:-
b) Tools of Evaluation:-
A) Qualitative Tools
I Observation:
Meaning:
- Instrument of assessing Personality
- To measure things very minutely
Definition:
- Measurement without instruments
Examples:
1) Teachers have listened to speeches & ranked student 1,2,3
2) Students have been labelled 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 Direct Observation:
- Valuable supplementary information
- Reliable & objective
- Study of individual in natural situation
- Used with children of all ages
- Used with training & experience
- Adaptable to both individual & group
- Detection of problems & corrective actions used in students work every situation & work habits.
Limitations & Demerits:
- Personal prejudices & bias of the observer
- No accurate observation is noted
- Small sample of students behaviour (Difficult to observe everything that a student does or says)
- Reveals the overt behaviour only (Behaviour that is expressed & not that is within)
Principles to be followed in making observation:-
- Observe whole situation
- Select one student to observe
- Observed in their regular activities
- Observation to be made over period of days
- Collect observation from several teachers.
Requisites of Good Observation:-
- Proper Planning
- Proper Execution
- Proper Recording
- Proper Interpretation
Planning of Observation:-
- Specific activities or unit of behaviour clearly defined.
- Selection of appropriate group of subjects
- Scope of observation
- Length, number & interval between periods
- Forms of recording
- Decide instruments
- Physical position
- Handy tools
Proper Execution of Observation:-
- Arrangement of special conditions
- Physical position
- Focussing attention
- Observing discreetly
- Proper handling of recording instrument
Utilization of training received in terms of expertners
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