This document compares and contrasts the arithmetic mean, median, and mode. It outlines the merits and demerits of each measure of central tendency. The arithmetic mean is summarized as the most stable and capable of algebraic treatment, as it uses all observations in its calculation. However, it can be affected by extreme values. The median and mode are not as capable mathematically but are not impacted by outliers in the same way. Overall, the document concludes that the mean is the best average.

1. ARITHMETIC MEAN
MERITS
 Simple to understand.
 Easy to calculate.
 Based on all observation.
 Capable for algebraic
treatment.
 It is more stable.
 It can be determined in most
of the cases.
 .

2. Demerits
 It is effected by extrme
values.
 Not suitable for ratios and
percentages.
 It cannot be calculated for
qualitative data.
 Misleading and absurd result
in some cases.
 It does not coincide with any
observed values

3. Compare Mean, Median and Mode
Mean is a mathematical average but
Median and mode are positional averages.
Mean is based on all observation while
median is the middle item and mode is
commonly found item.
Median and mode are values found in the
series but not mean.

4. •Median and mode can be graphically
located but not mean.
•Mean is affected by extreme item but
not median and mode.
•Mean is capable of further
mathematical treatment but not median
and mode

5. MEDIAN
MERITS
 It is very simple measure.
 Not affected extreme items.
 It can locate by a mere glance.
 It can be determined by
graphically.

6. Demerits
 Not based on all
observation.
 Not capable of algebraic
treatments.
 It requires arraying also.
 In the case of continuous
series interpolation
formula is used.

7. MODE
MERITS
 Can be located graphically.
 It is simple measure of central
tendency.
 Less affected by extreme
items
 It coincide with one of the
values of the series.

8. Demerits
 Not base on all
observations.
 Not capable of further
algebraic treatment.
 It is ill-defined in some
cases.
 Sometimes grouping to
identify the Modal
values.

9. BEST AVERAGE : MEAN
Easily calculated.
Simple to under stand.
Capable for algebraic treatment.

10. •Based on all observation.
•It can located without arranging the
data.
•It is stable fro sample to sample when
sample selected is sufficiently large.