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# Measures of central tendency

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### Measures of central tendency

1. 1. Measures of central tendency Mean Mode Median
2. 2. Mode  Distribution of application for admission to M.B.A. by discipline, Findings,  The commerce category is the most predominant. Discipline No. of students Science 55 Arts 60 Commerce 101 Engineering 45 Medical 5 Total 266
3. 3. Mode – Grouped data. Procedure, 1. Find the category or the class interval which has the greatest frequency. 2. The midpoint on this category is the mode. Age Group Frequency 1--20 15 21--40 32 41--60 54 61--80 30 81--100 19 Total 150
4. 4.  Mode frequency is 54 which is associated with the modal class interval of 41-60.The midpoint of this class interval is 50.5 i.e. (41+60)/2 = 50.5  Mode of this distribution is 50.5 Age Group Frequency 1--20 15 21--40 32 41--60 54 61--80 30 81--100 19 Total 150
5. 5. Use:  Useful measure for qualitative data.  Appropriate measure for nominal (qualitative) level of data.  E.g. include gender, nationality, ethnicity, language, genre, style, biological species, and form.  Application of data can be in distribution like ethnic classification of occupational classification.  For finding out the typical category.
6. 6. Median Grouped data  Procedure, = l + ((n/2 – cf) / f )*i  Find out mid point (n/2)  Find the class interval of mid point from the cumulative frequency column (cf)  l is the lower limit of the median category.  cf is the cumulative frequency up to but not median category.  i is the size(range) of the median class interval.
7. 7. AgeGroup Frequency CumulativeFrequencies 1--20 15 15 21--40 32 47 41--60 54 101 61--80 30 131 81--100 19 150 Total 150
8. 8. n/2= 150/2=75, Class interval= 41-60, f=54 l= 41, Cf=47, i=20 = l + ((n/2 – cf) / f )*i =41+((75-47)/54)*20 Mean =51.4 Use:  Used for ordinal (where the order matters but not the difference between values)or interval (where the difference between two values is meaningful)level data but not for nominal level data.
9. 9. Arithmetic mean = ∑ (fx) / n  X=any value  f= the frequency of a value  ∑=sum  n=the number of value Daily wages (f) Frequency (x) Fx 6 4 24 7 8 56 8 6 48 9 12 108 10 7 70 12 4 48 15 2 30 Total 43 384
10. 10.  Arithmetic mean= = ∑ (fx) / n  =384/43=8.9
11. 11. Grouped data = ∑ (fm) / n  m=midpoint of each class interval  f=frequency of a value  fm=midpoint multiplied by its frequency  n=number of cases
12. 12. =460/20=23. Score Frequency(f) Midpoint(m) fm 11--15 3 13 39 16--20 4 18 72 21--25 7 23 161 26--30 3 28 84 31--35 2 33 66 36--40 1 38 38 Total 20 460
13. 13. Choice of an appropriate average The choice depends upon the consideration of several factors:  The level of measurement  The research objective
14. 14. Level of measurement:  Mode requires only a frequency count, it can be applied to any set of data at the nominal, ordinal or interval level of data.  Median requires an ordering of items form the highest to the lowest or vice versa. Hence it can be obtained from an ordinal or interval level of data and not from nominal data like party affiliation, caste or religion.  Mean is exclusively restricted to interval data such as income, age, wage rate & test score.
15. 15. Research objective:  Mode is useful to find out most common category. E.g. test score, caste, age  Mean is useful for further mathematical manipulations.  Median is useful to find out mid values.