Measures Describing The Central Tendency Distributions- Average, Median, Mode, Biostatistics

1. Measures Describing
The Central Tendency
Distributions-
➢ Average,
➢Median,
➢Mode
Ravinandan A P
Assistant Professor
Sree Siddaganga College of Pharmacy
In association with
Siddaganga Hospital
Tumkur-02

2. Measures of Central Tendency
•The tendency of statistical data to get concentrated at certain
values is called the “Central Tendency”
•The various methods of determining the actual value at
which the data tend to concentrate are called measures of
central Tendency or averages.
•Hence, an average is a value which tends to sum up or
describe the mass of the data.

3. The Arithmetic Mean or simple Mean
• The arithmetic mean is the sum of all observations divided by the number
of observations. mean ; it is usually denoted by .
• Suppose the sample consists of birth weights (in grams) of all live born
infants born at a private hospital in a city, during a 1-week period.
• This sample is shown in the following table:
3265 3323 2581 2759 3260 3649 2841
3248 3245 3200 3609 3314 3484 3031
2838 3101 4146 2069 3541 2834

4. • It is written in statistical terms as:

5. • The arithmetic mean is, in general, a very natural measure of
central location.
• One of its principal limitations, however, is that it is overly
sensitive to extreme values.
• In this instance it may not be representative of the location
of the great majority of the sample points.

6. • For ex, if the 1st infant were in the above data happened to be a
premature infant weighing 500 gm rather than 3265 g, then the
arithmetic mean of the sample would be reduced to 3028.7 g.
• In this instance, 7 of the birth weights would be lower the arithmetic
mean, & 13 would be higher than the mean.
• It is possible in extreme cases for all but one of the sample points to
be on one side of the arithmetic mean.
• The arithmetic mean is a poor measure of central location in these
types of sample, since it does not reflect the center of sample.
• Nevertheless, the arithmetic mean is by far the most widely used measure
of central location.

7. • Merits of Mean:
✓It is a measure that can be calculated and is unique.
✓It is uses all the observations.
✓It is useful for performing statistical procedures such as comparing the
means from several data groups.
• Demerits of Mean:
✓It can not be representing as graphically.
✓It can not dealing with qualitative data, such as cleverness, humanity.
✓It will be wrong mean, if any of the observation missing or dropped.
✓If extreme class in open, it is hard to calculate.

8. Median
• The median is the middle of a distribution:
• half the scores are above the median and half are below the median.
• The median is less sensitive to extreme scores than the mean & this
makes it a better measure than the mean for highly skewed distributions.
• The median income is usually more informative than the mean income,
for example.
• The sum of the absolute deviations of each number from the median is
lower than is the sum of absolute deviations from any other number.
• Median is denoted by the symbol of M.

9. Eg:-3,4,4,5,6, 8,8,8 and 10 has median 6
5,5,7,9,11,12,15 & 18 has Median=9+11/2=10

11. • Merits of Median:
- It is very easy to calculate.
- It is rigidly defined.
- It is affected by the extreme values but is affected by the middle one or
two values.
- It can be calculated with open-end classes.
• Demerits of Median:
- If series has many observations, then it is very cumbersome to
calculate.
- It is not using all the observations.
When dealings with even number of observations, it involves only the mean
of two middle terms.

12. Mode
• The statistical mode is the number that occurs most frequently in a
set of numbers.
• Mode is denoted by the symbol of Z.
To find the mode of a group of numbers:
- Arrange the numbers in order by size.
- Determine the number of instances of each numerical value.
- The numerical value that has the most instances is the mode.
-There may be more than one mode when two or more numbers
have an equal number of instances and this is also the maximum
instances
-A mode does not exist if no number has more than one instance.

13. • The mode is not often used in biological or medical data.
• Find the modal values for the following data
a) 22, 66, 69, 70, 73. (no modal value)
b) 1.8, 3.0, 3.3, 2.8, 2.9, 3.6, 3.0, 1.9, 3.2, 3.5 (modal value = 3.0 kg)

14. • Merits of Mode:
• The mode is not unduly affected by extreme values.
• Most frequent value of the data set to be modal value.
• It is easy to calculate.
• Demerits of Mode:
• It is difficult to find a clearly defined mode.
• It is not based upon all the observations.
• There is no modal value, because the data set contains no values that occur
more than once.
• It is very difficult to interpret and compare, when data sets contain two,
three or many modes.

15. Thank you