Central tendency

Measures of central tendency

By

Lubna Toheed

Introduction                      

Measures of central tendency describe how the data cluster together around a central point. It is useful for making comparisons between groups of individuals or between sets of figures. It reduces a large number of measurements to a single figure, and thus makes comparisons easy.

Unfortunately, there is no single, standard procedure for determining central tendency. The problem is that no single measure will always produce a typical, representative value in every situation. Therefore, we use different ways to measure central tendency. There are three common measures of central tendency:

1.      The Mean or Average or arithmetic Mean,

2.      The median and ,

3.      The mode.

These three statistical measures are computed differently and have different characteristics. Here we will discuss ‘Mean’ and ‘Median’ only.

Mean         

The Mean of a distribution is known is “Arithmetic Mean”. Mean indicate the average value of the group. The Mean in each group or condition is calculated by adding up all the scores in a given condition, and then dividing by the number of participants in that condition.  It can be defined as “ the point on the scale of measurement obtained by dividing sum of all scores by the number of the scores.

Uses of Mean

1.       Mean is used when a reliable and accurate measure of central tendency is needed.

2.       Mean is used when the same scores are distributed symmetrically around the central point.

3.      Mean is used when the greatest stability is required

4.      Mean is used when other stastical calculation S.D./ M.D./ A.D. are to be completed.

5. Mean is used when we are having a series with no extreme items.

Calculation Of mean

Mean is calculated by two type of data

(1)    Ungrouped Data

(2)    Grouped Data

(1)Ungrouped Data

We use the following formula to find the mean of ungrouped data:

Where ,

∑ stand for ‘sum of’ or ‘Sum Total’

X Stand for the individual scores

N stand for total number of scores

Example:

Following are the marks of the students in the subject of mathematics.

Setudnts	marks
A B C D E	70 30 20 90 40
N==5	∑x = 250

(1)   Grouped Data

When the scores are large in number, the data is first grouped into the frequency distribution table and then the mean is calculated by using the following formulas:

a)Long Method

where ,

∑ stand for ‘ sum of’ or ‘ Sum Total”

f stand for frequency

x is the mid- point of class interval

N is the total number of scores

b) Short Method

 

Where,

C is correction factor with response to class interval

                                                    

A.M = Assumed mean

= Deviations of mid-point of the class interval from A.M divided by the size of class interval

F = frequency

I = size of the class interval.

Examples:                      

a)Using Long method

Calculate mean for  the following grouped data:

s.no	Class interval	Frequency
1 2 3 4 5	10-14 15-19 20-24 25-29 30-34	5 4 6 3 2
		N=20

              

The above data is consisted of class interval and frequencies. The size of each class interval is 5. It is difficult to know the aggregate of each class interval. So it is necessary to find out the mid- point of each class interval by using the following formula:

In the table below mid-points and fx for each class interval has been calculated

S.no	C.I	Class limits	f	x	fx
1 2 3 4 5	10-14 15-19 20-24 25-29 30-34	9.5-14.5 14.5-19.5 19.5-24.5 24.5-29.5 29.5-34.5	5 4 6 3 2	12 17 22 27 32	60 68 132 81 64
			N= 20

Putting values in formula:

        

b) Using Short Method

Using short method mean is calculated by taking the assumed mean from any class interval.

Suppose assumed mean (A.M) remain in the C.I. 22-24. The mid point of that C.I. is 22, is regarded as A.M.

While calculating of any class interval the formula used is:

 

       

Using short method mean is calculated by taking the assumed mean from any class interval.

Suppose assumed mean (A.M) remain in the C.I. 22-24. The mid point of that C.I. is 22, is regarded as A.M.

 

 

Properties of Mean

1.      The sum of deviations of all scores in a set from their Arithmetic Mean is “0”.

2.      The Sum of deviation from Arithmetic Mean is less then the sum of square of deviations from any other value.

3.      If each score of a series is subtracted by a constant quantity, the Mean will be as increased or decreased by the same quantity.

4.      If each score of a series divided or multiplied by a constant quantity, the mean will be multiplied or divided by the same quantity.

Merits of Mean

1.      It is rigidly defined.

2.      It is based on all the values.

3.      It is more stable than any other method of  average.

4.      It is relatively reliable.

5.      It is the center of gravity, balancing the values on either side of it.

6.      It has further algebraic treatment capacity.

Demerits of Mean

1.      It is highly affected by abnormal values.

2.      The loss of even a single observation makes it impossible to compute the aritmetic mean correctly.

Limitations

Mean can be very misleading if the distribution differs markedly from the normal and there are one or two extreme scores in one direction.

Median

The Median is the middle item when the data is listed in order. It is the point below which remain 50% of ‘N’ and above which remain the other 50% of N. So it is also called the 5^th percentile. Mean is called the positional average .The position refer to the place of the value in a series.

Median is used:

1. When  mid-point of the given distribution is to be found.
2. When the series contain extreme scores.
3. When there is open end distribution it is more reliable than Mean.
4. Mean cannot be calculated graphically, median can be calculated graphically.
5. For or articles that cannot be precisely measured.

Calculation Of mean

Mean is calculated for two types of data

(a)    Ungrouped Data

(b)    Grouped Data

(a)   Ungrouped Data

(1)    If there is an odd number of scores, then the median is simply the middle score, having an equal number of scores higher and lower than it.

The formula for the calculation of the  ungrouped data:

 

       

(2)  If there is an even number of scores. In that case, we work out the mean of     

(b)  Grouped data

When the score is in a continuous series, it is grouped into the frequency distribution table and the Median is then calculated by using formula:

                                                        

Example:

Calculate the Median from the following distribution table.

C.I.	50-54	55-59	60-64	65-69	70-74	75-79	80-84	85-89
f	8	12	24	16	32	20	11	5

Procedure to calculate median

1.      Locate the Median group  by N/2th

2.      Find out the cumulative frequencies

3.      Point out where N/2th score lies in which class interval

4.      Apply the Formula of Median.

S.no	C.I	C.I.	f	cf
1 2 3 4	50-54 55-59 60-64 65-69	49.5-54.5 54.5-59.5 59.5- 64.5 64.5- 69.5	8 12 24 16	8 8+12=20 20+24=44 44+16=60
5	70-74	69.5-74.5	32	60+32=92
6 7 8	75-79 80-84 85-89	74.5-79.5 79.5- 84.5 84.5-89.5	20 11 5	92+20=112 112+11=123 123+5 = 128
			N = 128

Where N/2 is 128/2 = 64

64 frequency remains in the class interval 69.5- 74.5 where the cumulative frequency is 92.

The Formula is:

                                                 

l = lower limit of class interval where N/2 lies

N = total number of frequencies

F = Total number of class frequencies of the C.I. above the C.I. where N/2 lies

fm = Actual number of frequencies of C.I. where N/2 lies

i = size of the C.I.

So, l = 69.5

       N = 128

        F =  60

        fm = 32

        

                                        

Merits of median

1.      It is easily calculated

2.      It is specially used in open-ended class interval

3.      It is not affected by the values of extreme items as it focuses only on scores in the middle of the distribution.

4.      It is the most appropriate average in dealing with qualitative data

Demerits of Median

1.      In calculating Median the data are to be arranged in descending or ascending order

2.      which is time consuming

3.      Since it is a positional average, its value is not determined by each and every observation.

4.      It may sometimes be indefinite, when the number of items in a median class is large.

5.      Median may sometimes be located at the point where the frequency may be quite small.

Limitations

1.      It is not suitable for further algebraic treatment.

2.      It can’t be used for computing other statistical measures such as S.D., co-efficient of correlation.

3.      The main limitation of the median is that it ignores most of the scores, and so it is often less sensitive than the mean.

4.      In addition, it is not always representative of the scores obtained, especially if there are only a few scores.

Summary

1.      Central tendency is the index which represents average performance of the group.

2.      Measures of central tendency describe how the data cluster together around a central point.

3.      There are three common measures of central tendency:

a)      Mean or Arithmetic mean

b)      Median

c)      Mode

6.      

 Bibliography

1.      Biswal, B. Stastics in Education & Psychology, Dominant Publishers and Distributers,

                                      New Delhi, 2006

2.      Text Book of Mathematics for class 10^th, KPK text book board Peshawar.

3.      http://statistics-in-education-and-psychological-studies.nuvvo.com/lesson/13349-measures-of-central-tendency

                                                                                       

ADJUSTMENT

ADJUSTMENT

(Home/Family and School)

By

Lubna Toheed

1.               Introduction:

You may have heard someone say that “somebody just doesn’t adjust to situation” or “somebody facing problem in adjustment”. Adjustment is a necessary characteristic to be able to live peacefully in this world.

Adjustment problem starts right from the birth of and continues till death, various situations arise at home. School, college, and workplace where we need to give up a little of our demands and accept what is present.

Adjustment is the process of arriving at a balanced state between the need of individual and their satisfaction. Home and school play pivotal role in the adjustment of an individual.

2.               What is adjustment?

The dictionary meaning of the word “adjustment” is, to fit, make suitable, adapt, arrange, modify, harmonize or make correspondent. Thus adjustment between two things means modify one or both of them to correspond to each other. For example: wearing of cloth according to the season.  As we can’t change the season so we have to modify our cloths.

The struggle between the needs of the individual and external forces is a continuous struggle since time immortal. According to the Darwin (1958) theory of evolution, those species which adapted successfully to the demands of living, survived and multiplied while others who did not, died out. Therefore adaptation or change in oneself according to the external environment is a basic need for survival.

However the concept of adjustment is not as simple as adaptation. Psychologist and scholars differ considerably in interpreting its meaning and nature.

James Drever defines adjustment as the modification to compensate for or meat special condition.

According to the Shaffer, L.S. “Adjustment is the process by which living organism maintain a balance between his needs and the circumstances that influence the satisfactions of these needs.

In the words of Coleman, James C., “Adjustment is the outcome of the individual’s attempts to deal with the stress and meet his needs: also his efforts to maintain harmonious relationships with the environment.

And according to the Carter V Good , “adjustment is the process of finding and adopting modes of behavior suitable to the environment or the change in the environment.

“Adjustment” can be defined as a process of altering one's behavior to reach a harmonious relationship with their environment. This is typically a response brought about by some type of change that has taken place. The stress of this change causes one to try to reach a new type of balance or homeostasis between the individual (both inwardly and outwardly), and with their environment.

3.               Areas of adjustment:

Adjustment in the case of individual consisted of personal as well as environmental components. These two aspects of adjustment can be further subdivided into smaller aspects of personal and environmental factors.

Broadly speaking there are three areas where an individual need to be adjusted to live a balance life. These are: Family and home, School, and Society.

Here we will discuss two areas: (1) Family and home, and (2) school.

3.1.          Adjustment at Family and Home:

An individual is not born adjusted or maladjusted, it is his physical, mental and emotional potentialities that are influenced and directed by the factors of environment in which he found himself that adjustment or maladjustment gradually develop.

The family is the oldest and the most important of all the institutions that man has devised to regulate and integrate his behavior as he strives to satisfy his basic needs. However, to understand the influence of the family on the child, it is important to understand the family and its functions.

It has been confirmed through various studies that if family relationship has been good, not only during childhood but also during adolescence, the person will develop into a well adjusted individual. One of the important roles of family is presumed to be the socialization of the child.

Home is first social institution where a child needs to be adjusted. When a child becomes aware of other individuals who comprise his social environment at home he tends to regard them as a mean through which he may attain personal satisfaction. He needs to be trained to modify his purely self centered interests and to cooperate in the activities of and for the welfare of others.

From the very beginning he imitates the speaking and eating habits of his family and gradually reflects attitudes learned in the home toward elders. Good or bad behavior that are exhibited at home are carried by the child into this relationships with persons outside the home. Thus the family attitudes become an important consideration in the adjustment of a child.

3.1.1.   Factors related to adjustment in the family:

According to the Continuity view, the role of the early parent-child relationship play basic role in constructing relations with people throughout the life span. Parental relation and the nature of the family process have a great effect on the adjustment process.

Parental divorce

The children of the divorce family show poorer adjustment than their counterparts in non divorced families. Those who have experienced multiple divorces are at greater risk.

Stepfamilies

Due to increase in the divorce rate and re-marriage the number of the step-families also increased. Like the divorced families, children and adolescents in the step families have also adjustment problems as compare to their counterpart in the biological families or non divorced families. Their problems are much like that of the children of divorced families- Academic problems, externalizing and internalizing problems, lower self esteem, delinquency and so on.

Single-mother family

 Children living in single-mother family structures were more likely to report maladjustment when compared to those living in non divorced- two biological parent family structures.

Working mothers

Working mother, who come to home after 2 o’ clock or after 4 o’ clock pay little attention to their children due to shortage of time and load of work. This situation effects the children in two ways: either they become adapted to the circumstances or they develop certain adjustment problems.

3.2.          Adjustment at school

As the children start school they face many challenges. Personal challenges occur as children take new identity at school. Children face the challenges to adjust to the strange building, new teachers, new academic activities, and they need to mix with the new and more diverse group of children.

At school, daily schedule is more structured, with more formal rules. Children are faced with large groups of children of different ages and size especially during assembly and playtime, and they are confronted with the challenges of making new friends. Toilets are often located away from classrooms and play areas. There are more buildings and bigger playgrounds. Thus a child confront with a totally new environment as compare to home. Successful adjustment to school largely depends on past experiences at home and on children skills and knowledge (Dockett, Perry & Tracey, 1997; Fabian, 2000).

When children exhibit a range of social skills associated with cooperation, initiating interactions or assertion, and self control, they are more likely to adjust easily to school. Difficulties are likely to arise when children are: non compliant; disorganized; distractible; or when they are anti social and have difficulty considering the rights of others (Margetts, 2002).

Adjustment to schooling is influenced by a variety of personal and family Characteristics, and societal trend.  It is the interaction of the child's personal characteristics and their experiences that ultimately determines how a child adjusts to school  (Margetts, 2002).

3.2.1.   Dimensions of Adjustment in School

Following are the important dimensions of adjustment in school.

1.         Adjustment to the building and school routine.

2.         Adjustment to academic, co-curricular activities.

3.         Psychological adjustment.

4.         Adjustment to and within the self.

5.         Social adjustment.

1.         Adjustment to the new building and school routine

This means that a child should not feel himself a stranger in the new school building. He should feel like home while playing in the play ground, using toilet, and performing different activities at school.

2.         Adjustment to Academic and  Co-curricular programs

 This includes Getting most out of specific studies and activities, to Overcoming learning problems and instructional difficulties, and to make satisfactory progress in exploratory experience.

3.         Psychological Adjustment

Development of good memory, desirable interest, good temper, and desirable      attitudes referred to the psychological adjustment of child. 

4.         Adjustment to and within Self

Adjustment to and within self means Self-understanding and acceptance, a Proper insight into needs, attitudes and values, overcoming emotional difficulties and Maintenance of health and personal hygiene.

5.         Social Adjustment

This means A Harmonious relationship with the students and teachers, Proper understanding of social needs, requirements and group goals, and meeting effectively to the social requirements of the home, peer groups, culture and the community.

3.2.2.   Factors effecting adjustment at school

1.         Proper training to Teachers

 Teacher’s training in educational psychology may help students in their adjustment. Teachers' personality and democratic attitude are also important factors which can promote adjustment in students.

2.         Adequate Curriculum

Curriculum should be planned, and transacted in such a way that it should fulfill psychological and social needs of students. Need fulfillment leads to better adjustment.

3.         Adequate Recreational Facilities

 Facilities, such as sports, library, debate and excursion may help students in their adjustment.

4.         Classroom climate

If the classroom climate is affectionate and cooperative enough, it can facilitate better adjustment in students.

5.         Proper relationships between administrations

 Cordial relations between the Principal and teachers, and teachers and teachers, and teachers and office staff also play an important role in creating harmonious and congenial environment in the school.

6.         Evaluation system of the school

 Evaluation should be rigid cum flexible. Too much subjectivity and unreliability should be avoided. Numerical marking should he avoided and grades should be given to students. Due to low marks, students lose confidence in their life which then affects in their mental health. The world 'fail' should not be used by the teachers

3.2.3.   The role of classroom teacher in student adjustment

The class room teacher plays the most strategic role to bring improvement in the class room environment and help the students in adjustment. He can perform the following role :

1.               Provide a classroom environment  where the children feel free to express themselves

2.               Develop in youngsters a sense self respect and self-esteem by complements for work well done.

3.               Accept the individual differences of students.

4.               Develops comprehensive cumulative records by collecting information through classroom sitting.

5.               Practices good mental health

6.               Participate and contributes to the effectiveness of case conferences.

7.               Teacher himself should adopt democratic and respective behavior.

            Adjustment as achievement

Adjustment can be interpreted as both process and the outcome of the process in the form of some achievements. When a poor child study in the corner of a play ground because in home he has not proper place to study he is said to be in the process of adjustment. As a result of that adjustment he achieves good grads in examination. Thus adjustment meant as an achievement means how the effectiveness with which an individual can function in changed circumstances.

            Adjustment a Continuous process

The process of adjustment is continuous. It starts at one’s birth and goes on without stop till one’s death. A person as well as his environment are constantly changing as also are his needs in accordance with the demands of the changing external environment. Consequently, the process or terms of an individual’s adjustment can be expected to change from situation to situation and according to Arkoff  (1968), there is nothing like satisfactory or complete adjustment which can be achieved once and for all time. It is something that is constantly achieved and re-achieved by us (Mangal,2006).

            Adjustment Mechanism

An adjustment mechanism is a device used by the individual to achieve satisfaction of the need indirectly. This helps reducing tensions and assists him in maintaining self-respect. With limits adjustment mechanisms are desirable and very helpful in dealing with frustration. Carried to extreme, they lead to behavior disorders. Following are adjustment mechanisms:

a)         Compensation. Compensation is a concept where the individual attempts to cover up his weakness in one area by exhibiting his strength in another. A student deficient in physical activities may compensate himself in showing good results in the academic field and vice versa.

b)         Identification. Identification is a concept when an individual attempts to identify himself with some successful person. To hide his own failures, a student may identify himself with his father and talk about his success.

c)         Rationalization. Rationalization means shifting of responsibility for our failures to factors outside it i.e. many students attribute their failure to the stiff question paper.

d)         Projection. This is a tendency to ‘push out’ upon another person one’s own unrealized, frustrated ambitions, or attribute to another one’s own faults. For example, school learners are often the victims of their parents’ projection of their former hopes for higher education and higher social status.

e)         Day-Dreaming. The imaginative fulfillment of needs is called day-dreaming. Day-Dreaming provides mental relief to an individual if it is done with limits. It becomes very detrimental when it is carried to excess (Aggarwal,1995).

            Characteristics of a Well-adjusted Person

A well-adjusted person is supposed to possess the following characteristics:

1.               Awareness of his own strengths and limitations. A well adjusted person knows his own strengths and weaknesses. He tries to make capital out of his assets in some areas by accepting his limitation.

2.               Respecting himself and others. The dislike of one-self is a typical symptom of maladjustment. An adjusted individual has respect for himself as well as for others.

3.               An adequate level of aspiration. His level of aspiration is neither too low nor too high in terms of his own strengths and abilities. He does not try to reach for the stars and also does not repent over selecting an easier course for his advancement.

4.               Satisfaction of basic needs. His basic organic, emotional and social needs are full satisfied or in the process of being satisfied. He does not suffer from emotional cravings and social isolation. He feels reasonably secure and maintains his self-esteem.

5.               Absence of critical or fault-finding attitude. He appreciates the goodness in objects, persons or activities. He does not try to took for weakness and faults. His observation is scientific rather than critical or punitive. He likes people, admires their good qualities, and wins their affection.

6.               Flexibility in behavior. He is not rigid in his attitude or way of life. He can easily accommodate or adapt himself to changed circumstances by making necessary changes in his behavior.

7.               The capacity to deal with adverse circumstances. He is not easily overwhelmed by adverse circumstances and has the will and the courage to resist and fight odds. He has an inherent drive to master his environment rather than to passively accept it.

8.               A realistic perception of the word. He holds a realistic vision and is not given to flights of fancy. He always plans, thinks and acts grammatically.

9.               A feeling of ease with his surroundings. A well-adjusted individual feels satisfied with his surroundings. He fits in well in his home, family, neighbourhood and other social surroundings. If a student, he likes his school, school-mates, teachers, and feels satisfied with his daily routine. When he enters a profession, he has a love for it and maintains his zeal and enthusiasm despite all odds.

10.            A balanced philosophy of life. A well-adjusted person has a philosophy which gives direction to his life while keeping in view the demands of changed situations and circumstances. This philosophy is centredaround the demands of his society, culture, and his own self so that he does not clash with his environment or with himself (Mangal, 2006).

Summary

Adjustment is not a simple term like adaptation or accommodation. It actually a behavioral process by which humans and other animals maintain an equilibrium among their various needs or between their needs and the obstacles of their environments.

The family is the oldest and the most important of all the institutions that man has devised to regulate and integrate his behavior as he strives to satisfy his basic needs. Successful adjustment to school largely depends on past experiences at home.

The class room teacher plays the most strategic role to help the students in adjustment.

Adjustment can be interpreted as achievement process.

Compensation,Identification,Rationalization,Projection,Day-Dreaming are the Important adjustment mechanisms.

 A well adjusted person pocess a balanced philosophy of life.

Bibliography

Aggarwa J. C. (1995). Essential Of Educational Psychology, VIKAS Publication, New Dehli.

Dockett, S., Perry, R. & Tracey, D. (1997). Getting ready for school. Paper presented at the Australian Association for Research in Education Annual Conference, Brisbane, December, 1997.

Fabian, H. (2000). A seamless transition. Paper presented at the EECERA 10th European Conference on Quality in Early Childhood Education, London, August 29 - September 1, 2000.

Mangle S. K .  (2006). Advanced Educational Psychology , Prentice  Hall of India, New Delhi.

Margetts, K. (2002). The developing child in today’s world: Issues and care in education. Educare News, Issue 127(July), 10-13

Santrock  W. J (2001).Adolescence ( 8th ed), McGraw-Hill Companies.

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