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SUMMARY- Measures of Central Tendency and Dispersion | Quantitative Aptitude for CA Foundation PDF Download

SUMMARY
The best measure of central tendency, usually, is the AM. It is rigidly defined, based on

all the observations, easy to comprehend, simple to calculate and amenable to

mathematical properties. However, AM has one drawback in the sense that it is very

much affected by sampling fluctuations. In case of frequency distribution, mean cannot

be advocated for open-end classification.
Median is also rigidly defined and easy to comprehend and compute. But median is not

based on all the observation and does not allow itself to mathematical treatment.

However, median is not much affected by sampling fluctuation and it is the most

appropriate measure of central tendency for an open-end classification.
Mode is the most popular measure of central tendency, there are cases when mode

remains undefined. Unlike mean, it has no mathematical property. Mode is also affected

by sampling fluctuations.
Relationship between Mean, Median and Mode

Mean – Mode = 3(Mean – Median)

Mode = 3 Median – 2 Mean
Relation between AM, GM, and HM

AM ≥GM ≥HM

GM and HM, like AM, possess some mathematical properties. They are rigidly defined

and based on all the observations. But they are difficult to comprehend and compute and,

as such, have limited applications for the computation of average rates and ratios and

such like things.

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FAQs on SUMMARY- Measures of Central Tendency and Dispersion - Quantitative Aptitude for CA Foundation

1. What are measures of central tendency?
Measures of central tendency are statistical measures that represent the center or average of a set of data. They provide a single value that summarizes the entire data set. The most common measures of central tendency are the mean, median, and mode.
2. How is the mean calculated?
The mean is calculated by summing up all the values in a data set and dividing it by the total number of values. It is also referred to as the average. For example, if we have a data set of 5, 8, 10, 12, and 15, the mean would be (5 + 8 + 10 + 12 + 15) / 5 = 10.
3. What is the median and how is it calculated?
The median is the middle value in a data set when the values are arranged in ascending or descending order. If the data set has an odd number of values, the median is the middle value. If the data set has an even number of values, the median is the average of the two middle values. To calculate the median, first arrange the data set in order and then find the middle value(s).
4. What is the mode and how is it determined?
The mode is the value that appears most frequently in a data set. It represents the value that occurs with the highest frequency. It is possible to have multiple modes in a data set or no mode at all. To determine the mode, identify the value(s) that appear most frequently in the data set.
5. How is the range calculated?
The range is a measure of dispersion and represents the difference between the maximum and minimum values in a data set. To calculate the range, subtract the minimum value from the maximum value. For example, if a data set has values ranging from 10 to 25, the range would be 25 - 10 = 15.
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