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Measures of central tendency - Relationship among the averages | 11th Business Mathematics and Statistics(EMS) : Chapter 8 : Descriptive statistics and probability

Chapter: 11th Business Mathematics and Statistics(EMS) : Chapter 8 : Descriptive statistics and probability

Relationship among the averages

In any distribution when the original items differ in size, the values of AM, GM and HM would also differ and will be in the following order AM ≥ GM ≥ HM

Relationship among the averages

In any distribution when the original items differ in size, the values of AM, GM and HM would also differ and will be in the following order

AM GM HM


 

Example 8.13

Verify the relationship among AM, GM and HM for the following data


Solution:


 

Example 8.14

A’s scooter gives an average of 40km a litre while B’s scooter gives an average of 30km a litre . Find out the mean, if

(i) each one of them travels 120 km.

(ii) the petrol consumed by both of them is 2 litres per head.

Solution:

(i)  Here the distance is constant. Hence harmonic mean is appropriate.


(ii) Here the quantity of petrol consumed is fixed i.e 2 litres. Here the arithmetic mean will give the correct answer.


Average speed = 35 km per litre.

 

Example 8.15

A person purchases tomatoes from each of the 4 places at the rate of 1kg., 2kg., 3kg., and 4kg. per rupee respectively .On the average, how many kilograms has he purchased per rupee?

Solution:

Since we are given rate per rupee, harmonic mean will give the correct answer.


 

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11th Business Mathematics and Statistics(EMS) : Chapter 8 : Descriptive statistics and probability : Relationship among the averages | Measures of central tendency

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11th Business Mathematics and Statistics(EMS) : Chapter 8 : Descriptive statistics and probability


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