STATISTICS

STATISTICS The numerical records of any event or phenomena are referred to as statistics. The data are the details in the numerical records or reports.

TYPES OF STATISTICS DESCRIPTIVE – It is concerned with the group of individuals actually observed. Statistics computed from these data or observations are called descriptive statistics. DESCRIPTIVE – It is concerned with the group of individuals actually observed. Statistics computed from these data or observations are called descriptive statistics. INFERENTIAL- This is used to search for general principles to be applied to a much larger domain beyond the group actually observed. INFERENTIAL- This is used to search for general principles to be applied to a much larger domain beyond the group actually observed.

NEED OF STATISTICS HELPFUL TO A TEACHER- It helps teachers in classifying a particular class into sub-groups for deciding about the method of teaching. Statistical methods are applied to get information from the available data to solve the practical problems. HELPFUL TO A TEACHER- It helps teachers in classifying a particular class into sub-groups for deciding about the method of teaching. Statistical methods are applied to get information from the available data to solve the practical problems. TOOL FOR SCIENTISTS- Psychologist take help of statistics for interpretation of behavioural data. In research work whether we explore new relationships or test theories our methods are largely statistical. TOOL FOR SCIENTISTS- Psychologist take help of statistics for interpretation of behavioural data. In research work whether we explore new relationships or test theories our methods are largely statistical.

DATA The data are the details in the numerical reports or records. The word data is a plural term as it usually refers to more than one observation or measure. The data are the details in the numerical reports or records. The word data is a plural term as it usually refers to more than one observation or measure.

TYPES OF DATA CONTINUOUS – We can have any number of sub-divisions in a continuous series and it is possible to get infinite number of in-between values very near to each other in the series. The physical measures such as metres, litres,Kilograms,hours and mental measures such as IQ fall into continuous series. CONTINUOUS – We can have any number of sub-divisions in a continuous series and it is possible to get infinite number of in-between values very near to each other in the series. The physical measures such as metres, litres,Kilograms,hours and mental measures such as IQ fall into continuous series. DISCRETE – In discrete data measurements are expressed in whole units e.g. number of members in a family, married and unmarried persons,number of girl and boy students in a class. DISCRETE – In discrete data measurements are expressed in whole units e.g. number of members in a family, married and unmarried persons,number of girl and boy students in a class.

SCORE A score is described as an interval which spreads from 5 unit below to 5 unit above the score. In a mental test, a score is a unit distance between the lower limit and the upper limit e.g. a score of 110 in an intelligence test denotes the score interval to 110.5, the exact midpoint of which is the score itself 110. A score is described as an interval which spreads from 5 unit below to 5 unit above the score. In a mental test, a score is a unit distance between the lower limit and the upper limit e.g. a score of 110 in an intelligence test denotes the score interval to 110.5, the exact midpoint of which is the score itself

FREQUENCY DISTRIBUTION Organizing the data by grouping the scores into categories of scores. When the number of measurements is small we keep the data ungrouped. When it is large we need to group it into a frequency distribution. Organizing the data by grouping the scores into categories of scores. When the number of measurements is small we keep the data ungrouped. When it is large we need to group it into a frequency distribution. By preparing Frequency distribution we arrange the data in systematic order by grouping the scores into classes. By preparing Frequency distribution we arrange the data in systematic order by grouping the scores into classes. The data become more organized, meaningful and Interpretable. The data become more organized, meaningful and Interpretable.

STEPS IN PREPARING THE FREQUENCY DISTRIBUTION DETERMINE THE RANGE – The range is defined as the highest score minus the lowest score. e.g. highest score is 86 and the lowest score is 22 the range is 64. DETERMINE THE RANGE – The range is defined as the highest score minus the lowest score. e.g. highest score is 86 and the lowest score is 22 the range is 64. DECIDE THE SIZE OF INTERVAL – The second step is to decide the size of the class interval or no. of groupings to be used in the distribution. The most commonly used size of class interval is 3,5,10 units. DECIDE THE SIZE OF INTERVAL – The second step is to decide the size of the class interval or no. of groupings to be used in the distribution. The most commonly used size of class interval is 3,5,10 units. NUMBER OF CLASS INTERVALS – The number of class intervals can be known by dividing the range by the size of the interval e.g. the range is 64 when divided by 5 it gives 12.8 or 13 class intervals. NUMBER OF CLASS INTERVALS – The number of class intervals can be known by dividing the range by the size of the interval e.g. the range is 64 when divided by 5 it gives 12.8 or 13 class intervals. TALLYING THE SCORES – The practice is to take one score at a time and record a tally mark for it against its appropriate interval. TALLYING THE SCORES – The practice is to take one score at a time and record a tally mark for it against its appropriate interval. SUMMING UP TALLIES AND FINDING OUT N – The sum of all the numbers in the frequency colomn gives N. SUMMING UP TALLIES AND FINDING OUT N – The sum of all the numbers in the frequency colomn gives N.

EXAMPLE CLASS INTERVAL ( CI) TALLY MARKS FREQUENCY (f) 85-89// /// //// // /// //// //// /// //// //// //// /// //// //2 50

EXERCISE Q1. For the following data draw frequency distribution using a class interval of 3 and 5. Marks of psychology students of class XI 72,69,84,82,67,73,72,63,78,81,70,76,76,75, 72,72,86,65,71,83,64,67,77,67,61.

MEASURES OF CENTRAL TENDENCY The measures of central tendency represent the central values of a group of individuals. The measures of central tendency represent the central values of a group of individuals. The important way of describing the scores of individuals in a group are by averages. The important way of describing the scores of individuals in a group are by averages. The average stands for any measure of central tendency. The average stands for any measure of central tendency. The commonly used measures of central tendency are Mean, Median and Mode. The commonly used measures of central tendency are Mean, Median and Mode.

USES OF CENTRAL TENDENCY MEASURES Indicator of group performance – A mass of individual scores of a group is reduced to a single score description by a measure of central tendency or an average. An average represents all the scores obtained by the group of individuals it is economical and meaningful. It is descriptive of the performance of group as a whole. Indicator of group performance – A mass of individual scores of a group is reduced to a single score description by a measure of central tendency or an average. An average represents all the scores obtained by the group of individuals it is economical and meaningful. It is descriptive of the performance of group as a whole. Comparability of two or more groups – By the use of averages we are able to compare two or more groups with regard to their typical performance. Comparability of two or more groups – By the use of averages we are able to compare two or more groups with regard to their typical performance. Estimates of population averages – Sample averages are close estimates of population averages. With our sample average we can generalize beyond samples and make predictions for the population. This is possible when our sample properly represents its population. Estimates of population averages – Sample averages are close estimates of population averages. With our sample average we can generalize beyond samples and make predictions for the population. This is possible when our sample properly represents its population.

THE MEAN OR ARTHMETIC MEAN Mean is the arithmetic average of the individual scores, it is the sum of the separate scores divided by their number. Mean is the arithmetic average of the individual scores, it is the sum of the separate scores divided by their number. The Mean is denoted by M The Mean is denoted by M (Here we will calculate Mean by three methods) Mean of Un grouped data Mean of Un grouped data Mean of grouped data by long – method Mean of grouped data by long – method Mean of grouped data by shortcut method or assumed mean method Mean of grouped data by shortcut method or assumed mean method

EXAMPLE Suppose five students of the group have scored following marks in psychology. Suppose five students of the group have scored following marks in psychology. X1= 53, X2 = 67, X3= 65, X4 = 58, X5= 62. M = € X M = € X N Where, M= Mean € = Sum total of € = Sum total of X = each individual score X = each individual score N = Number of measures N = Number of measures M = X1+X2+X3+X4+X5 N = = = 305 = = 61 = 61

Mean of ungrouped data Formulae of Mean for ungrouped data. Formulae of Mean for ungrouped data. M = € X M = € X N N Where, M= Mean € = Sum total of € = Sum total of X = each individual score X = each individual score N = Number of measures N = Number of measures

EXERCISE Q1. For the following data calculate Mean Marks of psychology students of class XI 72,69,84,82,67,73,72,63,78,81,70,76,76,75,72,72, 86,65,71,83,64,67,77,67,61. Q2.Calculate Mean for the marks obtained by 10 students in English 78, 24, 49,99,72,88,56,66,42,62 Q3. Calculate Mean of Marks obtained by 8 students in Physics. 72,81,69,78,74,91,88,89

MEAN OF GROUPED DATA BY LONG METHOD When the scores are too many we group them into a frequency distribution and apply any formula to compute the mean. When the scores are too many we group them into a frequency distribution and apply any formula to compute the mean. M = €fX NWhere, M = mean f = frequency of class intervals f = frequency of class intervals X= Midpoints of class interval X= Midpoints of class interval N = Number of measures N = Number of measures

Example Class interval (C.I mid-points f fX Class interval (C.I mid-points f fX

EXERCISE Q1. Calculate Mean of the following data using long method. SCORESFREQUENCY N = 200 N = 200

EXERCISE Q2. Calculate Mean of the following data using long method. SCORESFREQUENCY N = 125 N = 125

EXERCISE Q2. Calculate Mean of the following data using long method. SCORESFREQUENCY N = 50 N = 50

MEAN OF GROUPED DATA BY SHORT-CUT METHOD OR ASSUMED MEAN METHOD When the scores are too many we group them into a frequency distribution and apply formula of long method to compute the mean but sometimes data is too large to apply long method then we use assumed mean method. When the scores are too many we group them into a frequency distribution and apply formula of long method to compute the mean but sometimes data is too large to apply long method then we use assumed mean method. M = AM + ci M = AM + ciWhere, AM = Assumed mean c = €fx’ c = €fx’ NWhere, f = frequency of class intervals x’= Deviation of scores from the assumed mean. x’= Deviation of scores from the assumed mean. N = Number of measures N = Number of measures i = Size of Class- Interval i = Size of Class- Interval

Example Class interval fx’fx’ Class interval fx’fx’ N = 50

EXERCISE Q2. Calculate Mean of the following data using short-cut method or assumed mean method SCORESFREQUENCY N = 50 N = 50

EXERCISE Q2. Calculate Mean of the following data using short-cut method or assumed mean method. SCORESFREQUENCY N = 125 N = 125

EXERCISE Q1. Calculate Mean of the following data using short-cut method or assumed mean method SCORESFREQUENCY N = 200 N = 200

USE OF THE MEAN When the central point having maximum stability is needed. When the central point having maximum stability is needed. When the scores symmetrically fall around a central point i.e. the distribution of scores is not skewed. When the scores symmetrically fall around a central point i.e. the distribution of scores is not skewed. When further calculations like standard deviation and correlation coefficient are to be done. When further calculations like standard deviation and correlation coefficient are to be done.

USE OF THE MEDIAN When the exact 50 per cent point or the mid- point of the distribution is needed. When the exact 50 per cent point or the mid- point of the distribution is needed. When extreme scores are likely to remarkably to affect the mean. The median remains unchanged by the extreme scores When extreme scores are likely to remarkably to affect the mean. The median remains unchanged by the extreme scores When it is desired to know the position of an individual score in terms of its percentage distance from the mid-point of the distribution. When it is desired to know the position of an individual score in terms of its percentage distance from the mid-point of the distribution.

USE OF THE MODE When a rough and instant measure of the central point of the distribution is needed. When a rough and instant measure of the central point of the distribution is needed. When the measure of the central point is required to denote the most typical value or character of the group. When the measure of the central point is required to denote the most typical value or character of the group.