i) Draw percentage bar diagram from the following data. [5] Item Food Clothing Rent Fuel Education Miscellaneous : : : : : : : Expenditure (Rs.) 4500 3500 3000 2500 4500 5000 ii) Calculate the…

i) Percentage Bar Diagram

Step 1: Calculate the Total Expenditure

First, we sum up all the expenditure values to find the total expenditure.

$$4500+3500+3000+2500+4500+5000=23000\text{ Rs.}$$

Step 2: Calculate the Percentage for Each Item

Next, we calculate the percentage of each item's expenditure relative to the total expenditure.

$$\text{Percentage}=\left(\frac{\text{Expenditure}}{\text{Total Expenditure}}\right)\times 100$$

• Food: $$\left(\frac{4500}{23000}\right)\times 100=19.57\%$$

• Clothing: $$\left(\frac{3500}{23000}\right)\times 100=15.22\%$$

• Rent: $$\left(\frac{3000}{23000}\right)\times 100=13.04\%$$

• Fuel: $$\left(\frac{2500}{23000}\right)\times 100=10.87\%$$

• Education: $$\left(\frac{4500}{23000}\right)\times 100=19.57\%$$

• Miscellaneous: $$\left(\frac{5000}{23000}\right)\times 100=21.74\%$$

Step 3: Draw the Percentage Bar Diagram

Using the calculated percentages, we draw the percentage bar diagram below.

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ii) Calculation of Median

Step 1: Understand the Data

The given data is in the form of a cumulative frequency distribution (less than type). We need to find the median class.

Step 2: Calculate the Total Number of Students

The total number of students is the last cumulative frequency value, which is 90.

Step 3: Find the Median Position

The median position is given by:

$$\text{Median Position}=\frac{N}{2}=\frac{90}{2}=45$$

Step 4: Identify the Median Class

We look for the class where the cumulative frequency first exceeds 45.

• Cumulative frequency up to 70 marks is 48, which is greater than 45.
• Cumulative frequency up to 80 marks is 68, which is also greater than 45.

Thus, the median class is 70-80.

Step 5: Apply the Median Formula

The formula for the median in a grouped data is:

$$\text{Median}=L+\left(\frac{\frac{N}{2}-C}{f}\right)\times w$$

Where:

• $L$ = Lower limit of the median class = 70
• $N$ = Total number of students = 90
• $C$ = Cumulative frequency before the median class = 33
• $f$ = Frequency of the median class = 48 - 33 = 15
• $w$ = Width of the median class = 10

Substitute the values:

$$\text{Median}=70+\left(\frac{45-33}{15}\right)\times 10$$

$$\text{Median}=70+\left(\frac{12}{15}\right)\times 10$$

$$\text{Median}=70+0.8\times 10$$

$$\text{Median}=70+8=78$$

Final Answer: The median is 78.