Measures of central tendency
Also called: Averages · Topic: Economic Data: Census, NSS, Surveys and Statistical Tools · NCERT: Class 11, Ch 5 "Measures of Central Tendency"; Class 11, Ch 8 "Use of Statistical Tools"
Meaning
Measures of central tendency, also called averages, sum up a whole set of data in one typical value. Nobody can remember thousands of incomes, but one average income is easy to remember and compare. There are three common averages:
- Arithmetic mean: X̄ = ΣX/N, the total divided by the number of items.
- Median: the middle value once the data are arranged in order.
- Mode: the value that occurs most often.
Each suits a different kind of data. An average alone can mislead, so it should be read together with the spread of the data.
Example
In NCERT, Baiju owns 1 acre in Balapur (Buxar, Bihar). Comparing his holding with the mean, median and mode of the 50 farmers' holdings shows where he stands. In another NCERT project, 100 households spent a mean of Rs 104 per household per month on toothpaste.
Don't confuse with
- Measures of dispersion: an average gives the centre of the data. Dispersion shows how widely the values are spread around that centre.
Related concepts
- Arithmetic mean
- Weighted arithmetic mean
- Median
- Quartiles
- Decile
- Percentiles
- Mode
- Bimodal and multimodal distribution
- Modal class
- Relative position of mean, median and mode