Question

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

Marks	Frequency
140 – 144	3
144 – 148	9
148 – 152	24
152 – 156	31
156 – 160	42
160 – 164	64
164 – 168	75
168 – 172	82
172 – 176	86
176 – 180	34

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). 

Join A₁B₁, B₁C₁, C₁D₁, D₁E₁, E₁F₁, F₁G₁, G₁H₁, H₁I₁ and I₁J₁ with a free hand to get the ‘more than type’ series

The two curves intersect at point L. Draw LM ⊥ OX cutting the x-axis at M. Clearly, M = 166cm 

Hence, median = 166 cm