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Draw cumulative frequency curve (ogive) for each of the following distributions: (i) $$\begin{tabular}{|l|l|l|l|l|l|l|} \hline Class Interval & $10-15$ & $15-20$ & $20-25$ & $25-30$ & $30-45$ & $35-40$ \\ \hline Frequency & 10 & 15 & 17 & 12 & 10 & 08 \\ \hline \end{tabular}$$ (ii) $$\begin{tabular}{|l|l|l|l|l|l|} \hline Class Interval & $10-19$ & $20-29$ & $30-39$ & $40-49$ & $50-59$ \\ \hline Frequency & 23 & 16 & 15 & 20 & 12 \\ \hline \end{tabular}$$
Draw cumulative frequency curve (ogive) for each of the following distributions:
(i) $$\begin{tabular}{|l|l|l|l|l|l|l|} \hline Class Interval & $10-15$ & $15-20$ & $20-25$ & $25-30$ & $30-45$ & $35-40$ \\ \hline Frequency & 10 & 15 & 17 & 12 & 10 & 08 \\ \hline \end{tabular}$$
(ii) $$\begin{tabular}{|l|l|l|l|l|l|} \hline Class Interval & $10-19$ & $20-29$ & $30-39$ & $40-49$ & $50-59$ \\ \hline Frequency & 23 & 16 & 15 & 20 & 12 \\ \hline \end{tabular}$$
CBSE | Class 10 | Graphical Representations | ICSE | Maths | Selina
Draw cumulative frequency curve (ogive) for each of the following distributions:
(i) $$\begin{tabular}{|l|l|l|l|l|l|l|} \hline Class Interval & $10-15$ & $15-20$ & $20-25$ & $25-30$ & $30-45$ & $35-40$ \\ \hline Frequency & 10 & 15 & 17 & 12 & 10 & 08 \\ \hline \end{tabular}$$
(ii) $$\begin{tabular}{|l|l|l|l|l|l|} \hline Class Interval & $10-19$ & $20-29$ & $30-39$ & $40-49$ & $50-59$ \\ \hline Frequency & 23 & 16 & 15 & 20 & 12 \\ \hline \end{tabular}$$

Solution:
(i)
$$\begin{tabular}{|l|l|}
\hline Class Interval & Frequency \\
\hline 10-15 & 10 \\
\hline 15-20 & 15 \\
\hline 20-25 & 17 \\
\hline 25-30 & 12 \\
\hline $30-35$ & 10 \\
\hline $35-40$ & 08 \\
\hline
\end{tabular}$$
Selina Solutions Concise Class 10 Maths Chapter 23 ex. 23 - 5

Steps of construction:

(a) By taking suitable scales, mark the class intervals on $\mathrm{x}$-axis and the frequencies on $\mathrm{y}$-axis.

(b) We need to construct rectangles with class intervals as bases and corresponding frequencies as heights.

(c) Now, join the mid-points of the rectangle to obtain the ogive.

(ii)
$$\begin{tabular}{|l|l|l|l|}
\hline Class Interval (Inclusive) & Class Interval (Exclusive) & Frequency & Cumulative \\
\hline $10-19$ & $9.5-19.5$ & Frequency \\
\hline $20-29$ & 19.5-29.5 & 23 & 23 \\
\hline $30-39$ & 29.5-39.5 & 16 & 39 \\
\hline $40-49$ & 39.5-49.5 & 20 & 54 \\
\hline $50-59$ & 49.5-59.5 & 12 & 74 \\
\hline & & Total & 86 \\
\hline
\end{tabular}$$
Selina Solutions Concise Class 10 Maths Chapter 23 ex. 23 - 6
Steps of construction:

(a) We need to convert the data into exclusive form. [Here, adjustment factor = 0.5]

(b) By taking suitable scales, mark the class intervals on x-axis and the frequencies on y-axis.

(c) Now, construct rectangles with class intervals as bases and corresponding frequencies as heights.

(d) Now, join the mid-points of the rectangle to obtain the ogive.

i

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