Graphical Representations

Draw an ogive for each of the following distributions:
(i) $$\begin{tabular}{|l|l|l|l|l|l|} \hline Marks Obtained & less than 10 & less & less & less & less \\ \hline No. of Students & 8 & 25 & 38 & 50 & than 50 \\ \hline \end{tabular}$$
(ii) $$\begin{tabular}{|l|l|l|l|l|l|l|l|} \hline Age in years (less than) & 10 & 20 & 30 & 40 & 50 & 60 & 70 \\ \hline Cumulative Frequency & 0 & 17 & 32 & 37 & 53 & 58 & 65 \\ \hline \end{tabular}$$

Solution: (i) $$\begin{tabular}{|l|l|} \hline Marks Obtained & No. of students (c.f.) \\ \hline less than 10 & 8 \\ \hline less than 20 & 25 \\ \hline less than 30 & 38 \\ \hline less than 40 & 50...

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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) $$\begin{tabular}{|l|l|l|l|l|l|} \hline Class Interval & $10-19$ & $20-29$ & $30-39$ & $40-49$ & $50-59$ \\ \hline Frequency & 23 & 16 & 15 & 20 & 12 \\ \hline \end{tabular}$$

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 $35-40$...

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Draw histograms for the following frequency distributions:
(i) $$\begin{tabular}{|l|l|l|l|l|l|} \hline Class Interval & $30-39$ & $40-49$ & $50-59$ & $60-69$ & $70-79$ \\ \hline Frequency & 24 & 16 & 09 & 15 & 20 \\ \hline \end{tabular}$$
(ii) $$\begin{tabular}{|l|l|l|l|l|l|l|l|} \hline Class Marks & 16 & 24 & 32 & 40 & 48 & 56 & 64 \\ \hline Frequency & 8 & 12 & 15 & 18 & 25 & 19 & 10 \\ \hline \end{tabular}$$

Solution: (i) $$\begin{tabular}{|l|l|l|} \hline Class Interval (Inclusive form) & Class Interval (Exclusive Form) & Frequency \\ \hline $30-39$ & 29.5-39.5 & \\ \hline $40-49$ & 39.5-49.5 & 24 \\...

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Draw histograms for the following frequency distributions:
(i) $$\begin{tabular}{|l|ccccc|c|} \hline Class Interval & $0-10$ & $10-20$ & $20-30$ & $30-40$ & $40-50$ & $50-60$ \\ \hline Frequency & 12 & 20 & 26 & 18 & 10 & 6 \\ \hline \end{tabular}$$
(ii) $$\begin{tabular}{|l|l|l|l|l|l|} \hline Class Interval & $10-16$ & $16-22$ & $22-28$ & $28-34$ & $34-40$ \\ \hline Frequency & 15 & 23 & 30 & 20 & 16 \\ \hline \end{tabular}$$

Solution: (i) $$\begin{tabular}{|l|l|} \hline Class Interval & Frequency \\ \hline $0-10$ & 12 \\ \hline 10-20 & 20 \\ \hline 20-30 & 26 \\ \hline $30-40$ & 18 \\ \hline 40-50 & 10 \\ \hline 50-60 &...

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