(i)Transform the following data (population) into frequency distribution of 5 equal size class intervals and draw frequency curve than define shape of the distribution.
1.5 4.3 3.4 3.6 2.9 3.3 3.9 3.1
1.3 3.1 3.7 4.4 3.2 4.1 1.9 3.4
4.7 3.8 3.2 2.6 3.9 3.0 4.2 3.5
2.5 4.3 3.4 3.6 2.9 3.3 3.9 3.1
2S.3 3.1 3.7 4.4 3.2 4.1 1.9 3.4
4.7 3.8 3.2 2.6 3.9 3.0 4.2 3.5
(ii)Find Arithmetic mean, Geometric mean and Harmonic mean of the frequency distribution and prove that:
A.M≥G.M.≥H.M
(iii)Transform frequency distribution into standard normal variate ( z-distribution)
and prove that mean of the distribution is zero and standard deviation is one.
