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
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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