Dr. Ansari Khurshid Ahmed - Characteristics of Mean- Illustrations.pptx

Measure of Central Tendency is an important topic to be taught at B.Ed. level. Mean is a reliable measure of central tendency having some very important characteristics. In the given ppt, some important characteristics of Mean are highlighted with the help of simple illustrations which will be helpful for the students of B.Ed. to comprehend the theory of Mean.

1. Measures of Central Tendency ( Characteristics & Limitations of Mean ) (Illustrations) For B.Ed. Students

2. Dr. Ansari Khurshid Ahmed Associate Professor Marathwada College of Education Chh . Sambhajinagar (Aurangabad)

3. Characteristics of Mean Mean is Sensitive to the size of Extreme Scores. Illustration: X: 10 20 30 40 50 60 70 80 90 M = 450/9 = 50 , Mdn = 50 X: 14 20 30 40 50 60 70 80 95 M = 459/9 = 51 , Mdn = 50 Result : Mean changes due to change in the size of extreme scores where as Median remains unchanged.

4. Characteristics of Mean Sum of Deviations of all the scores from Mean is always zero. Illustration: Deviation of Score from Mean = x x = X – M Score X: 10 20 30 40 50 60 70 80 90 M = 450/9 = 50 Deviation x : (10-50) (20-50) (30-50) (40-50) (50-50) (60-50) (70-50) (80-50) (90-50) Deviation x : -40 -30 -20 -10 00 10 20 30 40 Ʃx = 0 Sum of deviations Ʃx = 0 Result : Sum of deviations of all the scores from Mean is always Zero.

5. Characteristics of Mean Mean is algebraic in nature. Illustration: Mean of Combined Group = (N 1 M 1 + N 2 M 2 + --- )/(N 1 + N 2 ---) = (40 × 60 + 50 × 70)/(40 + 50) = 65.56 Discussion : If Mean of two or more than two groups are given then Mean of the combined group can be determined with the help of a formula as mentioned in the example. This is not possible in case of Median and Mode. Mean N Combined Mean Group 1 60 40 65.56 Group 2 70 50

6. Characteristics of Mean When a constant number is added to each score of the series, Mean changes by that constant number. Illustration: X 1 : 10 11 12 13 14 15 16 17 18 M 1 = 126/9 = 14 X 2 = X 1 + 5 : 15 16 17 18 19 20 21 22 23 M 2 = 171/9 = 19 = 14 + 5 = M 1 + 5 Discussion : Mean of First Series of scores is 14. The second series is obtained by adding a constant number 5 to each score of the first series. The Mean of the second series is 19 which can be obtained by adding the constant number 5 to the Mean of First Series.

7. Characteristics of Mean When a constant number is added to each score of the series, Mean changes by that constant number. Illustration: X 1 : 10 11 12 13 14 15 16 17 18 M 1 = 126/9 = 14 X 2 = X 1 +(- 5) : 5 6 7 8 9 10 11 12 13 M 2 = 81/9 = 9 = 14 - 5 = M 1 - 5 Result : Mean of First Series of scores is 14. The second series is obtained by adding a constant number (-5) to each score of the first series. The Mean of the second series is 9 which can be obtained by adding the constant number (-5) to the Mean of First Series.

8. Characteristics of Mean When each score of the series is multiplied by constant number, Mean changes by multiple of that constant number. Illustration: X 1 : 10 11 12 13 14 15 16 17 18 M 1 = 126/9 = 14 X 2 = X 1 × 5 : 50 55 60 65 70 75 80 85 90 M 2 = 630/9 = 70 = 14 × 5 = M 1 × 5 Discussion : Mean of First Series of scores is 14. The second series is obtained by multiplying each score of the first series by a constant number 5. The Mean of the second series is 70 which can be obtained by multiplying Mean of the First Series by the constant number 5.

9. Characteristics of Mean When each score of the series is multiplied by constant number, Mean changes by multiple of that constant number. Illustration: X 1 : 10 20 30 40 50 60 70 80 90 M 1 = 450/9 = 50 X 2 = X 1 × (1/ 5) : 2 4 6 8 10 12 14 16 18 M 2 = 90/9 = 10 = 50 × 1/5 = M 1 × 1/5 Discussion : Mean of First Series of scores is 50. The second series is obtained by multiplying each score of the first series by a constant number 1/5. The Mean of the second series is 10 which can be obtained by multiplying Mean of the First Series by the constant number 1/5.

10. Limitations of Mean Mean is a not reliable measure of central tendency when the series of scores contains few very high or very low scores at its extremes. Illustration: X 1 : 10 11 12 13 14 15 16 17 18 Mean = 126/9 = 14 Median = 14 X 2 : 10 11 12 13 14 15 16 17 90 Mean = 198/9 = 22 Median = 14 Discussion : Mean of First Series of scores (which is not skewed) is 14 which is acceptable representative of all the scores. But the second series of scores is skewed as 8 out of total 9 scores are at the lower end of the series whereas only one score 90 is at the upper end of the series. There is a huge gap between 17 and 90. The mean of second series is 22 which does not seem to be a representative of majority of scores whose values are less than 22. But Median is 14 which can be considered as representative of the given series of scores as 90 is an exceptional case.

11. Limitations of Mean Mean is unreliable measure of central tendency in case of skewed distribution. Illustration: (Skewed Distribution) A Frequency Distribution in which scores are piled up either at the upper end or lower end of the distribution is called as skewed distribution. Mean = 73.5 Median = 76.17 Discussion : In this case, there are more number of cases at the upper end of the table hence Measure of Central Tendency should be one from higher values of X. Mean is 73.5 whereas Median is 76.17 which is more close to higher value of X. Hence here Median seems to be good representative of 20 score than Mean. Class Interval (X) Frequenncy (f) 80 - 89 8 70 – 79 6 60 – 69 3 50 – 59 2 40 - 49 1 N = 20

12. Limitations of Mean When scores of the series are expressed in the form of Rank or Grade then Mean can not be determined. Illustration: X : A B D C A C E D A B D (Scores in the form of Rank or grade) Discussion : In order to compute Mean, scores of the series are to be added. But grades or ranks can not be added that is why Mean in such cases can not be determined.

13. Limitations of Mean Mean can not be accurately determined in case of open end table. Illustration: (Open End Table) A table that does not have intervals of specified length at upper end or lower end ( or both the ends) of the table. Discussion : In order to compute Mean, mid-point of each class interval is required. The mid-point of the class interval ‘Less than 50’ can not be determined accurately. Hence Mean of the given open end table can not be determined accurately. Class Interval (X) Frequency (f) 80 - 89 6 70 – 79 8 60 – 69 10 50 – 59 5 Less than 50 11