Question

Q. a) Find out the average rate of increase in population which in the first decade has increased 20%, in the second 25% and in third 44% respectively. b) Find out the average speed of a person who rides the first mile at the rate of 8 miles an hour, the second mile at the rate of 7.5 miles an hours and the third mile at the rate of 5.5 miles an hour. c) What was the relation between A.M, G.M and H.M prove the relation for following data? Also write merit and demerit of H.M 21,45,78,89,109,54,97,34,67,123

Answer 1

a)

Suppose the initial population is 100 units.

After first year = 100*1.2 = 120

After second year = 120*1.25 = 150

After the third year = 150*1.44 = 216

The total percentage increase in three years is (216 - 100) / 100, which is 116%.

Average = 116 / 3 = 38.67%

b)

Average Speed = Total Distance / Total Time

Total distance = 3 miles

Total time = 1 / 8 + 1 / 7.5 + 1 / 5.5 = 0.125 + 0.133 + 0.1818 = 0.44

Average speed = 3 / 0.44 = 6.81 miles/hour

c)

The relation is

AM * HM = GM**2

The data is -

21,45,78,89,109,54,97,34,67,123

AM = Sum of all / number of observations = 717 / 10 = 71.7

GM = (21*45*78*89*109*54*97*34*67*123)**0.1 = 63.4

HM comes out to be 56.06.

AM * HM = GM**2

71.7 * 56.06 = (63.4)**2

71.7 * 56.06 = 4019.56

4019.56 = 4019.56

It is proved.