If you want to understand Mean, Median and Mode. I tried to make it as simple as possible.

1. Central Tendency
Mr Upendra Singh
Lecturer Dept. of Psychiatric Social Work
Dr Ram Manohar Lohia
New Delhi, India

2. Introduction
• Measures of central Tendency
• Statistical average
• Indicates the point on which data clusters.
• Representative of the entire mass of the data.

3. Introduction
• The value of the measure of central tendency is
two folded:
1. It is an average representing all of the scores by
the group & gives a concise description of the
performance of the group as a whole.

4. Introduction
2. It enables to compare two or more groups.
• There are three measures of central
tendency:-
– Mean
– Median
– Mode

5. Mean
• Average
• Sum of the scores divided by their members.
• M = ∑X / N
– N = No. of measures in a series
– X= Scores or measures
– ∑ = Sum of

6. Mean
• Mean for group data
• M = ∑fx / N
• ∑fx = sum of midpoints weighted by their
frequencices

7. Mean
• Mean through short cut method
• M = AM – Ci
• C = ∑fx’ / N
• AM – assumed mean
• C – correction
• i = class interval

8. Mean
• It is the simplest measure.
• Widely used.
• It is amenable to algebraic treatment.
• It is relatively permanent measure.
• It is affected by unduly extreme items.
• Thus, may lead to wrong impression.

9. Median
• It is the value of the middle item of any given series,
when arranged in ascending and descending order of
magnitude.
• It divides the series into two halves.
• > 50% & < 50%

10. Median – Formula
• Mdn = N + 1 / 2
• Mdn = l + (N/2 – F / fm) I
• l = exact lower limit of the class interval upon which the
median lies
• N/2 = one-half of the total no. of scores
• F = sum of scores on all intervals below l
• fm = frequency within the interval upon which the median
falls
• i = length of class interval

11. Median
• It is a positional average.
• Used in the quantent of qualitative phenomena of
behavioral field.
• Not used if scores needs to be assigned relative
importance.
• Not frequently used.

12. Mode
• The most frequently occurring value in a series.
• In a distribution it is the item around which
maximum scores concentrates.
• It is positional average.
• Not affected by the values of extreme items.
• Useful in all situations.
• Study of popular size.

13. Mode
• Not amenable to algebraic treatment.
• Remains indeterminate when there lies 2 or more
model values in a series.
• Unsuitable in cases where items need to be given
relative importance.
• In ungrouped data mode is that single measure or
score which occurs most frquently.

14. Mode
• In grouped data mode is the midpoint of that class
interval which contains the largest frequency.
• Mode = 3Mdn – 2Mean

15. THANK YOU!