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 â‰¥ GM â‰¥ 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 *â‰¥* GM *â‰¥* HM*

**Example 8.13**

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

*Solution:*

**Example 8.14**

Aâ€™s scooter gives an average of
40km a litre while Bâ€™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.

âˆ´ 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.

Tags : Measures of central tendency , 11th Business Mathematics and Statistics(EMS) : Chapter 8 : Descriptive statistics and probability

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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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