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Answer 1

Question : -

The following distribution table shows the daily profit (in rupees) of 100 shops of our village

$\begin{tabular}{|c|c|c|c|c|c|c|} \cline{1-7} Profit of each shop &0-50 & 50-100 & 100-150 & 150-200 & 200-250 & 250-300 \\ \cline{1-7} No. of shops & 10 & 16 &28 & 22 &18 & 6 \\ \cline{1-7} \end{tabular}$

ANSWER

Given : -

$\begin{tabular}{|c|c|c|c|c|c|c|} \cline{1-7} Profit of each shop &0-50 & 50-100 & 100-150 & 150-200 & 200-250 & 250-300 \\ \cline{1-7} No. of shops & 10 & 16 &28 & 22 &18 & 6 \\ \cline{1-7} \end{tabular}$

Required to find : -

• Construct Ogive curve for the following data ?

Solution : -

$\begin{tabular}{|c|c|c|c|c|c|c|} \cline{1-7} Profit of each shop &0-50 & 50-100 & 100-150 & 150-200 & 200-250 & 250-300 \\ \cline{1-7} No. of shops & 10 & 16 &28 & 22 &18 & 6 \\ \cline{1-7} \end{tabular}$

The above data will be modified and can be written as

$\begin{tabular}{|c|c|} \cline{1-2} Profit of each shop & No. of shops \\ \cline{1-2} (0-50) & 10 \\ \cline{1-2} (50-100) & 16 \\ \cline{1-2} (100-150) & 28 \\ \cline{1-2} (150-200) & 22 \\ \cline{1-2} 200-250 & 18 \\ \cline{1-2} 250-300 & 6 \\ \cline{1-2} \end{tabular}$

Now,Since, we need to prepare Ogive curves now, let's add one more tabel to the above data i.e. cumulative frequency !

Cumulative frequencies are of 2 types;

LCF (Lesser Cumulative Frequency)

GCF (Greater Cumulative Frequency)

Since, these are 2 types the Ogive curves are also of 2 types;

Lesser than Ogive

Greater than Ogive

For this let's explore both the Ogive curves ! Lesser than Ogive For less than Ogive the table needs to be prepared as follows;

$\begin{tabular}{|c|c|c|c|} \cline{1-4} Profit of each shop & No. of shops & Lesser Cumulative Frequency & upper boundary - LCF \\ \cline{1-4} (0-50) & 10 & 10 & (50,10) \\ \cline{1-4} (50-100) & 16 & 26 & (100,26) \\ \cline{1-4} (100-150) & 28 & 54 & (150,54) \\ \cline{1-4} (150-200) &22 & 76 & (200,76) \\ \cline{1-4} 200-250 & 18 & 94 & (250,94) \\ \cline{1-4} 250-300 & 6 & 100 & (300,100)\\ \cline{1-4} \end{tabular}$

For lesser than Ogive curve refer to the attachment !

Greater than Ogive

For the greter than Ogive the table needs to be prepared as follows;

$\begin{tabular}{|c|c|c|c|} \cline{1-4} Profit of each shop & No. of shops & Greater Cumulative Frequency & lower boundary - GCF \\ \cline{1-4} (0-50) & 10 & 100 & (0,100) \\ \cline{1-4} (50-100) & 16 & 90 & (50,90) \\ \cline{1-4} (100-150) & 28 & 74 & (100,74) \\ \cline{1-4} (150-200) & 22 & 46 & (150,46) \\ \cline{1-4} 200-250 &18 & 24 & (200,24) \\ \cline{1-4} 250-300 & 6 &6 & (250,6)\\ \cline{1-4} \end{tabular}$

For greater than Ogive curve refer to the attachment !