Question

The following is the frequency distribution of blood pressure of 100 patients.

Blood pressure (in suitable units )	110-115	115-120	120-125	125-130	130-135
No. of patients	2	35	52	8	3

(i) Draw a less-than cumulative frequency curve and find the reading below which blood pressure readings of 50% patients were observed.

(ii) Draw the histogram and hence, find the approximate mode .

Answer 1

To draw the less-than type cumulative frequency curve we prepare the following table .

Class interval	Frequency fi	Upper boundary ui	Less-than cumulative frequency (Fi )
-	-	110	0
110-115	2	115	2
115-120	35	120	37
120-125	52	125	89
125-130	8	130	97
130-135	3	135	100
Total	100 = N	-	-

We take upper class boundaries (u_i ) on the X-axis and the less-than cumulative frequencies (F_i ) on the Y-axis .
Thus, we plot the points (110,0), (115,2), (120,37), (125,89), (130,97), (135,100).
We join these points by a smooth free-hand curve and get the less-than type frequency curve .



Median is the middle-most item in the ordered arrangement of data. Therefore, it is the value of the $\frac{\mathrm{N}}{2}$th item.
Accordingly, we mark the middle-most observation, i.e. 50 on the Y-axis .
In the above graph, it is A . Draw a line segment AB parallel to the X-axis. Suppose the line segment cuts the less-than cumulative frequency curve at B.
The point B has X-co-ordinate as median and Y-co-ordinate as $\frac{\mathrm{N}}{2}$.We draw a line segment BC perpendicular to the X-axis. The foot of the perpendicular is the median.
Here the median is 121 units

(ii) We will find the mode from the graph with the following steps.
(a) Draw the histogram to represent the data.
(b) Locate the modal class, pre-modal class and post-modal class .
(c Join the right-hand top vertices of the modal class (C) and pre-modal class (a) by a straight line .
(d) Join the left-hand top vertices of the modal class (B) and post-modal class (D) by a straight line .
(e) Let the point of intersection of AC and BD be E .
(f) Draw a segment EF perpendicular to the X-axis .
(g) The foot of the perpendicular, F, is the mode .