central tendency, biostatistics

1. A Brief Overview On Central Tendency

2. What is central tendency?
 Central tendency is a descriptive summary of a
dataset through a single value that reflects the center
of the data distribution.
 The central tendency is one of the most quintessential
concepts in statistics.
 Although it does not provide information regarding
the individual values in the dataset, it delivers a
comprehensive summary of the whole dataset.

3. Measure of Central Tendency
Generally, the central tendency of a
dataset can be described using this 3
measurement :
Central
Tendency
Mean
Median
Mode
Central Tendency of a dataset can
also be measured by
Midrange

4. Measuring Mean
 The mean represents the average value of the dataset.
 It can be calculated as the sum of all the values in the dataset divided by the number of values.
 In general, it is considered as the arithmetic mean.
Mean value, 𝑥̅ =
𝑥1+𝑥2+⋯+𝑥𝑛
𝒏
Here,
𝑥1 + 𝑥2 + ⋯ + 𝑥𝑛= sum of the values
n= total number of value in a dataset
The formula of mean value,
𝒙 =
𝜮𝒙
𝒏
Example:
Dataset : 76, 43, 55, 29, 40, 66, 26, 76, 91
x
̅ = (76 + 43 + 55 + 29 + 40 + 66 + 26 + 76 + 91) / 9 = 55.78

5. Measuring Mean by Python

6. Measuring Median
• The middle value in a dataset that is arranged in ascending order (from the smallest value to the largest value).
• If a dataset contains an even number of values, the median of the dataset is the mean of the two middle values.
For ODD number of dataset, the median value
is the most middle value.
Example :
Dataset : 2, 17, 6, 8, 9, 3, 11, 20, 15,
In ascending order : 2, 3, 6, 8, 9, 11, 15, 17, 20
2, 3, 6, 8, 9, 11, 15, 17, 20
The middle value is : 9
For EVEN number of dataset, the median value
is calculated by :
The sum of two middle values / 2
Example :
Dataset : 2, 17, 6, 8, 9, 3, 11, 20, 15, 30
In ascending order : 2, 3, 6, 8, 9, 11, 15, 17, 20, 30
2, 3, 6, 8, 9, 11, 15, 17, 20, 30
The middle value is : (9 + 11) / 2 = 10

7. Measuring Median by Python
For Odd Number of Dataset For Even Number of Dataset

8. Measuring Mode
The mode is the most frequently occurring value in the dataset.
It’s possible to have no mode, one mode, or more than one mode.
Example for NO MODE value in
a dataset:
Dataset : 43, 55, 29, 40, 66, 26,
76, 91
In the given dataset there is no
repeated value, so this dataset
has no mode value.
Example for ONE MODE value
in a dataset:
Dataset : 43, 55, 29, 40, 66, 26,
76, 91, 29
In the given dataset the “29” is
repeated one time.
So, the mode value = 29
Example for MORE THAN ONE
MODE value in a dataset:
Dataset : 43, 55, 29, 40, 43, 66, 26,
76, 91, 32, 26
In the given dataset the “43” is
repeated one time and “26” is
repeated one time.
So, the mode value = 43 and 26

9. Measuring Mode by Python

10. Measuring Mid-range
 In statistics, the mid-range or mid-extreme is a measure of central tendency of a sample defined as the
arithmetic mean of the maximum and minimum values of the data set.
The formula for calculating Mid-range:
Mid – range = (largest value of the dataset + smallest value of a dataset) / 2
Example:
Dataset : 76, 43, 55, 29, 40, 66, 26, 76, 91
Mid-range = (91+26) / 2 = 58.5

11. THANK YOU