Question

Using the frequency distribution table given below, draw 'less than ogive'. Then from the ogive, find: [6 MARKS]
i) lower quartile
ii) upper quartile
iii) semi-interquartile range
$\begin{array}{cc}Classinterval& Frequency\\ 5-10& 3\\ 10-15& 4\\ 15-20& 6\\ 20-25& 9\\ 25-30& 7\\ 30-35& 1\end{array}$

Answer 1

Formula: 2 Marks
Table: 2 Marks
Graph: 2 Marks

We prepare the cumulative frequency table as given below:
$\begin{array}{ccc}Classinterval& Frequency& Cumulative\\ & & frequency\\ 5-10& 3& 3\\ 10-15& 4& 7\\ 15-20& 6& 13\\ 20-25& 9& 22\\ 25-30& 7& 29\\ 30-35& 1& 30\end{array}$
The points to be plotted are (5, 0), (10, 3), (15, 7), (20, 13), (25, 22), (30, 29) and (35, 30). Plotting these points on a graph paper and joining by a freehand curve, we get the cumulative frequency curve (a 'less than ogive') as given below:

i) To find the lower quartile $Q_1$, we locate $\frac{n}{4}$, i.e., 7.5 on y-axis and proceed horizontally to meet the ogive. From this point, draw a perpendicular to meet the x-axis.
$\therefore$ From figure $Q_1=15.5$

ii) To find the upper quartile $Q_3$, we proceed similarly as in (i) taking
$\frac{3n}{4}=\left(\frac{3\times 30}{4}\right)=22.5$ to obtain
$Q_3=25.5$, as shown in the graph.

iii) Semi-interquartile range $=\frac{Q_3-Q_1}{2}$
$\frac{25.5-15.5}{2}=5$