Measurement of Central tendency Hand written notes

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Central tendency refers to the statistical measurement that determines the location of the average value of a given data set. In other words, it describes the central point of the distribution or the most representative value of the data. Three important measures of central tendency are-


1. Mean: Mean is the sum of all the values in a dataset divided by the total number of values. It is the most commonly used measure of central tendency. Mean is denoted as “μ” (mu) and is calculated by the formula: 


μ= ∑ (Xi) / N, 


where Xi is the value of a variable, ∑ Xi is the sum of all the values, and N is the total number of observations.


2. Median: Median is the middle value in a dataset. To find the median, the data should be arranged in order from smallest to largest. The median is the value that appears in the middle, i.e., exactly half of the values are above the median, and the other half are below it.


If there is an even number of observations, the median is the average of the two middle values. Median is denoted as “Md.”


3. Mode: Mode is the value that appears most frequently in a dataset. In some cases, a dataset may have more than one mode. In that case, the data is said to be bimodal. Mode is denoted as “Mo.”


These measures of central tendency are used to describe various aspects of a dataset. Mean is the most commonly used measure, as it incorporates all the values in the data, but it can be affected by outliers. Median is not affected by outliers, and it is useful when the data is not normally distributed. Mode is useful when the data is clustered around a specific value.


In conclusion, measuring central tendency is essential in statistics. It helps to understand the distribution of the data in a more straightforward and concise manner. Measures like mean, median, and mode provide valuable information about the central location of the data set, which can help in making appropriate conclusions and predictions.


1. Mean

2. Median

3. Mode

4. Range

5. Interquartile Range (IQR)

6. Standard Deviation

7. Variance

8. Skewness

9. Kurtosis

10. Confidence Interval

11. Outlier

12. Frequency distribution

13. Normal Distribution

14. Histogram

15. Box plot/Whisker plot

16. Quartiles

17. Percentiles

18. Mode

19. Arithmetic Mean

20. Geometric mean.