Question

From the following data, draw the two types of cumulative frequency curves and determine the median:

Answer 1

(i) Less than series:

We plot the points A(144, 3), B(148, 12), C(152, 36), D(156, 67), E(160, 109), F(164, 173), G(168, 248) and H(172, 330), I(176, 416) and J(180, 450). 

Join AB, BC, CD, DE, EF, FG, GH, HI, IJ and JA with a free hand to get the curve representing the ‘less than type’ series.

(ii) More than series:

Now, on the same graph paper, we plot the points A₁(140, 450), B₁(144, 447), C₁(148, 438), D₁(152, 414), E₁(156, 383), F₁(160, 277), H₁(168, 202), I₁(172, 120) and J₁(176, 34). 

The two curves intersect at point L. Draw LM ⊥ OX cutting the x-axis at M. 

Clearly, M = 166cm 

Hence, median = 166cm